I dont know a specific computer, but ASUS makes computers specifically for gaming, my friends have them and they work amazingly, I have a macbook which works really well to but, not many games are for mac.
Well I think Chrome is best, easy to use and pretty customizable and very fast. Ive found Internet Explorer is not the fastest and is not at all great. I have not used Fire Fox much, but have heard positive feedback. I think chrome is great with being able to connect your google account which can be used for various different purposes. Personally I would choose chrome, but it is up to you.
Like NetherJoe said make sure meta-INF is gone. Also try getting mod loader or forge if it still doesn't work. There is an installer for forge, check here: http://www.minecraftforge.net/forum/ind ... 075.0.html Also make sure that both minecraft and reis is the same version, so 1.6.1 and 1.6.1 or 1.6.2 and 1.6.2. Not Having minecraf 1.6.1 and rei's 1.6.2.