Sensitive skin? This suggests to me that carts (?) are causing you problems? What are the problems?
In most cases a DE (or straight once mastered) will solve a lot of the problems because it is sharper and produces less irritation once your technique is good and you know your beard growth (beard mapping).
Thick beard? I have coarse, strong hair according to my barber - this just impacts blade life more than use IMHO.
Others might comment - I know that @alfredus has a thick beard (?)
- properly map your beard? I have a suspicion, that a couple of whiskers around your adams apple grow in a different direction, therefore you shave them first XTG/ATG and cause bleeding/ingrowns
- don't chase the dragon BBS, go for a DFS or even SAS, until you have everything under control
- lather quality!!! most underrated topic there, but if you don't have slickness etc, you won't have great shaves.
- very light prep - you want to just wet your whiskers, but NOT soften the (already sensitive) skin. I just wash with cold water and a good soap - none of that shave after the shower business
- don't overwork your lather on your face, unless you know what you are doing - yes a boar mashed into your face can give you already ingrown hair/burn
Blades: as @Mark1966 always says, it is the razor/blade combo, not the blade alone. But if you have indeed a coarse bears, sensitive skin and a weird beard growth (welcome to the "it sucks" club) - for me the following things work: mild razor, with smooth blades: for me Voskhod and Lada's, if you have a very mild razor, then PolSilver SI work as well. As a razor: the Edwin Jagger/Muhle 88de works very well, or a vintage HD rocket or a vintage non-alu Tech - or you can come to the world of stainless steel, but it costs...
Again don't chase the BBS (at first) - I need 4 passes - after 1 day or after 5 - I need 4 passes for a BBS and if you don't have your beard perfectly mapped this will lead to a disaster.
I am the same as Chris, except I have Just ordered my first razor being a Rockwell 6S and thanks to @Korbz I have a couple of packets of Voskhod blades to try but it would be good to try some others too.