I don't mind the bloat of the latest Ubuntus. The only thing that really annoys me about them is that they removed a lot of what used to be default. Aside from that, the bloat is hardly noticeable. It doesn't run any less smoothly for me unless I'm using a Live CD. If it pains you that much, go with Windows 7.
Anyway, my recommendation for CPU is to wait for Haswell, which should be out by June. If you can't wait until then, Ivy Bridge should be fine. Some mid-grade i3 or low-end i5 should suit your needs. Even an Ivy Bridge Pentium or Celeron should be enough, but if you want to do 10-bit 1080p, you'll probably want to move up the chain.
Video cards I can't give you any recommendations for, but if your gaming does not get really intense, you can keep it cheap here.
For RAM, 8GB DDR3 is standard these days. Just make sure that the RAM you buy clocks at a speed equal or higher than the CPU's memory speed, and get something that's rated an average of no less than 5 eggs on Newegg with at least 20 ratings. G.Skill is a big name for RAM.
Be sure to get an SSD for your boot disk (do your research). Prices on those have dropped to a point where it doesn't make sense to boot off of an HDD just to save a few bucks. Intel is best for reliability but their performance is a little lacking. Corsair makes stuff that is better for performance. I personally like G.Skill's stuff, though they are a smaller name for SSDs. Be sure to also grab an HDD for data storage.
For PSU, Corsair is solid, as are ThermalTake and Antec. Again, do your research.
For motherboards, generally the big names are ASUS, Gigabyte, and Asrock. Make sure you get the right socket for your CPU, and pick something that works for what you want to do (PCI-e for your video card, at least four slots for RAM, etc.). As always, do your research.
Skip the sound card entirely if you are any less than an audiophile, which most are. Onboard sound is usually good enough.
As for case, see what reviewers rated well and what you think looks nice. Lian Li is a top manufacturer for cases. Close behind it are Corsair and Antec.
If you want an actual build, there are a few people around the forums (like kitamesume, for example) who will put a list of parts together for you. You should also lower your budget constraint to around $800, because "some gaming, anime, movies etc." should not need much more than $800.