I have a few NYX eyeshadows that are almost as good as my Urban Decay ones, and a couple blushes that are pretty nice too. Rimmel makes really good bronzer that's pretty cheap if you're into that. I really think it's worth it to get a good foundation. MAC is really good, and their foundations are cheaper than other higher end brands. I have both the Studio Fix fluid and powder, and I really love both products. Pretty much any product has the potential to break you out; there's just so many ingredients in them that it's impossible to really be certain what you will or won't be sensitive to. No makeup is good for your skin, but if you wash it off really well and take good care of you're skin it'll be fine.
Also, ELF has an HD finishing powder that is just as good as the MUFE and MAC ones for less than $7 I think, and I also have one of the flat head powder brushes from their studio line that works well for applying liquid foundation (it was only like $3 too). As for mascara, I really like Cover Girl. I've used one that I think was called Lash Blast (something like that...) and I really liked it.