For straight razors the ratio of blade thickness to blade width (heighth) is approx 1:3.5 or 1:4. This HAS to be done in order to ensure the right final edge geometry. For example, I have a .25" thick razor that has a blade about .8" tall. When I first started making them, I thought the spine had to be really thin. WRONG. The spine needs to be thick, and for the best edges, hollow ground. Older straight razors and kamisori were indeed wedges. I like hollow grind. Just remember the ration of between 1:3.5 and 1:4.
I'm sorry, for your steel, that's up to you. If you want carbon steel, I would go with a hypereutectoid, such as 1095, 52100, W2 (mine is W2), or the like. For stainless, I would love to make one out of AEB-L, but any quality stainless should work well.