It depends how much you care about future proofing. If you do want future-proofing, then go for Intel, although AMD will give you a lot more performance for a budget build if you do not care about future proofing, since Intel does that better.
I highly recommend you use the NZXT Source 210. Its a fantastic case for only $40 and its comes in both black and white.
For the CPU I would recommend an APU, the AMD A10 Godavari is the best, and will run a lot of games at 1080p without a dedicated GPU
Since this is a non-future proofing parts list I am putting together, the motherboard only need to be good enough to support the components that are being put into it. I would recommend the MSI A6HM-E33. Its not pretty, but it will get the job done along with overclocking capability for only $50.
G. Skill RAM is well priced and just works, so going for a single G. Skill Ripjaws 8GB stick is a solid option and allows you to upgrade to 16GB.
Going for an SSD and then later adding an HHD for mass storage is a good option, and I would recommend going for a Kingston 240GB, which is cheap and I have had good experience with Kingston SSD's.
For any build a cheap-o PSU leads to many headaches, so you should go for a solid one. Antec PSU's are my personal favorite(I have one in my main build) and are reasonably priced. The Antec HCG is a solid option and will ensure you don't have any power problems.
Cooler Master Hyper Evo 212 is a solid option and will get the job done.
The total comes out to $515. The leftover money could be used to purchase a keyboard and mouse if you do not already have one. If you do not have a monitor or OS, your going to need a little more money. If you could expand your budget just a little more, you could buy a GPU and I would recommend the EVGA or Asus 750 TI. Its a fantastic entry level card and I have used it myself, its performance is absolutely amazing and it would do even better with an APU in there. If this doesn't fit your needs very well, check out Linus's 2015 Holdiay Buyers Guide here.