Every so often I see a thread where someone asks for recommendations on the best soap or cream for a beginner to wet shaving. People provide their opinions. I shall take a different approach. Rather than recommending a soap/cream, I will provide the requirements that I believe must be fulfilled by a suitable candidate for a first soap. Although I will mention examples they are only that - the omission of a product from the discussion most likely only means that I have not tried it. An additional advantage is that if the beginner does not think that a requirement applies to them they can disregard it.
To specify requirements you must have an overarching objective in mind. My objective is this: that the beginner should reliably be able to produce a lather that gives them a pleasant shave. Notice the modesty of this goal: I do not aim to provide them with the best lather, or the best value lather. The key here is to identify products that are most likely to give an adequate lather for as many beginners as possible.
I wish to avoid the beginner being disheartened by a poor experience, thinking that a satisfactory experience is beyond them and giving up. My theory is that soaps and creams are consumable - as long as the beginner continues wet shaving there will be a second soap. And a third. Once the beginner knows what they can expect from a soap and has developed their lathering technique they are free to chase perfection in whatever way will please them.
So, to business.
The first requirement is that the soap be well known to the forum. This is important because should the beginner feel that their technique is lacking, or that the product seems a bit "off", diagnosis or reassurance can be provided by forumites with first-hand experience. In practice this means that the use of local artisans should be avoided for a first soap. I do not mean to discourage shavers from supporting local businesses - after getting the hang of building a lather I believe that the opportunity to use such local businesses is part of the joy of wet shaving. But I have seen too many poor reviews of products from small businesses that mostly make bath soap and try branching out into shaving soap without a firm understanding of the difference between the two products.
The second requirement is that the product must have been found to perform well (or at least adequately) by almost all who have tried it. No product can have totally unanimous reviews, but hanging around B&B reveals some products are more problematic than others. This is not about individual experience, but the aggregate experience of the board. Remembering the overall goal, I am quite willing to forego the chance of recommending the best possible product if it reduces the probability of discouragement and reversion to canned goo. I would argue that this rules out Mitchells Wool Fat and Williams. I know that "The Fat" has many adherents and it could make a fine second soap - but not the first. I would also avoid the hard soaps from Taylor's of Old Bond Street, Geo F Trumper, Truefitt and Hill and D R Harris due to various poorly-reviewed reformulations, although their shaving creams are generally well though-of.
The third requirement is that the product must be of low cost to acquire. I choose my words carefully because this is not about cost per shave. I am sure that according to your calculations your puck of Martin de Candre works out at a lower cost than Arko, but it is still daunting as a beginner to be told that you must pony up north of $50 for soap when there is a brush and razor to be purchased as well. You can get a perfectly decent lather for a fraction of the outlay. This rules out Martin de Candre, and also Saponificio Varesino and Acqua di Parma. This will also depend where you are in the world: for example, in the UK it rules out many US artisans because they are often marked up compared to more local products.
The fourth requirement is that the product must be of uncontroversial scent. I know that it matters not a jot to the physical act of shaving, but it is important to the shaving experience. A beginner who reverts to canned goo because they cannot stand the smell of the product they are using is as lost to us as one who reverts due to poor performance. Again, this is down to the aggregate opinion of the board, not individuals. This turns out to be something of a giant-killer, as Arko and (tallow) Tabac are frequently recommended for their performance but are unquestionably polarising on the issue of their scent (if indeed one can describe the odour of urinal cakes as a scent (just joshing...)).
The fifth requirement is that the product should not cause an adverse reaction to the skin. Doubtless you can find a story of someone having a bad reaction to every product on the market, but there do seem to be some repeat offenders out there. It is almost certainly to a minority of users (it would represent a major failing on the part of the manufacturer otherwise), but why take the risk when there are lass controversial choices? The two I see most often mentioned are people getting fragrance burn from soaps by Ariana and Evans, and bad skin reactions to Proraso white (the latter baffles me because it is supposed to be their "sensitive" formulation). I've also seen some people report that Sandalwood brings them out in a rash.
So where does that leave us? Still with lots of options. Proraso Green and Blue, Speick, La Toja, Cella, Haslinger. If you are in the US, Stirling. In the UK, Cyril Slater and the creams from the "big four" above. And that's only what I can name off the top of my head. Feel free to suggest any other products that meet the above requirements, especially for regions outside of the US and UK.
To specify requirements you must have an overarching objective in mind. My objective is this: that the beginner should reliably be able to produce a lather that gives them a pleasant shave. Notice the modesty of this goal: I do not aim to provide them with the best lather, or the best value lather. The key here is to identify products that are most likely to give an adequate lather for as many beginners as possible.
I wish to avoid the beginner being disheartened by a poor experience, thinking that a satisfactory experience is beyond them and giving up. My theory is that soaps and creams are consumable - as long as the beginner continues wet shaving there will be a second soap. And a third. Once the beginner knows what they can expect from a soap and has developed their lathering technique they are free to chase perfection in whatever way will please them.
So, to business.
The first requirement is that the soap be well known to the forum. This is important because should the beginner feel that their technique is lacking, or that the product seems a bit "off", diagnosis or reassurance can be provided by forumites with first-hand experience. In practice this means that the use of local artisans should be avoided for a first soap. I do not mean to discourage shavers from supporting local businesses - after getting the hang of building a lather I believe that the opportunity to use such local businesses is part of the joy of wet shaving. But I have seen too many poor reviews of products from small businesses that mostly make bath soap and try branching out into shaving soap without a firm understanding of the difference between the two products.
The second requirement is that the product must have been found to perform well (or at least adequately) by almost all who have tried it. No product can have totally unanimous reviews, but hanging around B&B reveals some products are more problematic than others. This is not about individual experience, but the aggregate experience of the board. Remembering the overall goal, I am quite willing to forego the chance of recommending the best possible product if it reduces the probability of discouragement and reversion to canned goo. I would argue that this rules out Mitchells Wool Fat and Williams. I know that "The Fat" has many adherents and it could make a fine second soap - but not the first. I would also avoid the hard soaps from Taylor's of Old Bond Street, Geo F Trumper, Truefitt and Hill and D R Harris due to various poorly-reviewed reformulations, although their shaving creams are generally well though-of.
The third requirement is that the product must be of low cost to acquire. I choose my words carefully because this is not about cost per shave. I am sure that according to your calculations your puck of Martin de Candre works out at a lower cost than Arko, but it is still daunting as a beginner to be told that you must pony up north of $50 for soap when there is a brush and razor to be purchased as well. You can get a perfectly decent lather for a fraction of the outlay. This rules out Martin de Candre, and also Saponificio Varesino and Acqua di Parma. This will also depend where you are in the world: for example, in the UK it rules out many US artisans because they are often marked up compared to more local products.
The fourth requirement is that the product must be of uncontroversial scent. I know that it matters not a jot to the physical act of shaving, but it is important to the shaving experience. A beginner who reverts to canned goo because they cannot stand the smell of the product they are using is as lost to us as one who reverts due to poor performance. Again, this is down to the aggregate opinion of the board, not individuals. This turns out to be something of a giant-killer, as Arko and (tallow) Tabac are frequently recommended for their performance but are unquestionably polarising on the issue of their scent (if indeed one can describe the odour of urinal cakes as a scent (just joshing...)).
The fifth requirement is that the product should not cause an adverse reaction to the skin. Doubtless you can find a story of someone having a bad reaction to every product on the market, but there do seem to be some repeat offenders out there. It is almost certainly to a minority of users (it would represent a major failing on the part of the manufacturer otherwise), but why take the risk when there are lass controversial choices? The two I see most often mentioned are people getting fragrance burn from soaps by Ariana and Evans, and bad skin reactions to Proraso white (the latter baffles me because it is supposed to be their "sensitive" formulation). I've also seen some people report that Sandalwood brings them out in a rash.
So where does that leave us? Still with lots of options. Proraso Green and Blue, Speick, La Toja, Cella, Haslinger. If you are in the US, Stirling. In the UK, Cyril Slater and the creams from the "big four" above. And that's only what I can name off the top of my head. Feel free to suggest any other products that meet the above requirements, especially for regions outside of the US and UK.