your pc is a nice build right now but in a few years it'll be a bit lacking.
I'd say if you are doing so little with your pc an SSD is a great idea, personally. Your processor will be ok for a few years. The GFX card is good right now but also not future proof.
Personally I store a lot of things so I got 2TB on my latest pc to be "future proof", but skipped the SSD since I play different games quite often, didn't want to buy a 500+ space as that would've upped my pc's cost by over 50%, and can't be bothered switching my SSD files every few weeks.
Also you can get a slightly stronger pre-built PC from dell than what DZcreeper linked for £500~ which should be similar figure to the $800. I got an I7-3770k, 12 gb ram, nvidia gtx 670 2gig (don't like amd's after my old pc had a lot of problems due to the card on some games, but they should be fine for minecraft), 2 tb (personal preference, after 3 months I've already used about 600gig after using 50gig on the fresh setup),
You can use an I5 if budget is an issue with gaming pc, but if you are playing games which utilize CPU then it's just as important (and often more unless the game are brand new graphics strainers, i.e. you are buying new games 3 years from now) as the GPU. Memory is a basic.
Simply put it sounds like an SSD would be the perfect thing for you. I'd also warn that if you play any ports - although it doesn't sound like you will - I would hold off on the windows 8. Not all the driver updates are out yet.