Lots of great advice has already been offered. I would also mention you are far far from the only person who has encountered this issue—search for “neck” and I’m sure you can find even more suggestions.
For what it’s worth, I could never get close shaves on my neck with a cartridge. Now, with a DE I have to approach conservatively—but 4 out of 5 shaves I get a very close finish with no irritation. I get the rare ingrown around the Adam’s Apple, but never any razor burn. Better preparation can make a big improvement (hot towel, brush and lather being made on the face) even with a cartridge razor—but DE is simply miles better.
For what it’s worth, I could never get close shaves on my neck with a cartridge. Now, with a DE I have to approach conservatively—but 4 out of 5 shaves I get a very close finish with no irritation. I get the rare ingrown around the Adam’s Apple, but never any razor burn. Better preparation can make a big improvement (hot towel, brush and lather being made on the face) even with a cartridge razor—but DE is simply miles better.