Best straight razor: too many good ones; and everyone has their favourites.
Learning curve: well there is one, but if you have patience and are willing to spend a little time, it's well worth it.
cost: to start out, bare minimum $75 for decent gear (about $130 for a nice starter set
. A razor and strop absolutely neccessary. A good brush and soaps are highly recommended.
Some words of advice. Stay the hell away from ebay (for now); there is a ton of crap and knockoffs that you don't want to have near your face, and, takes some experience to tell the difference from just pictures. Also, checkout www.straightrazorplace.com Tons of info there. Check the forums too, way more info there. Once you get the jist, sign up and introduce yourself. Lots of sellers of some of the highest quality gear hang out there, and, could surely hook you up.