New mid range pc

[tmac]

The pc I'm using at present is an OC Spinosaurus that I bought 6 years ago and it still performs fairly well but I'm thinking it should either be replaced or updated and I'm not sure of which to do.
I'm not much of a gamer, only play WoW, but would like to maybe play some of the new first person shooter type of game.
So my question is would I get more for my money but using the existing case, ss drive etc and buy a bundle or just but a ready built one.
I have budgeted on spending around £800 but less is always good.

Thanks for having a look and your opinions would be appreciated.

 

[tmac]

Guys sorry for the delay in replying but work really does get in the way and I'd like to thanks LewisRaz and lee32uk for their input.

My system at present is
Motherboard Gigabyte Z77 chipset
Intel i5 2500K 3.7 running at 4.2
Crucial MX100 512 Gb
8Gb memory
N'vidia GTX460
Generic DVD re-writer
750W PSU
Antec case with 2 x cooling fans.

So I would be better to change the PSU and the only things I would be able to reuse are the case, SDD and DVD re-writer.

 

[tmac]

The psu is just an off the shelf one and I'm not sure it would support the new ranges of gpu.
I like the idea of just a graphics card upgrade if it would do the job as todays upgrades are always better value in a months time.
Thanks to all for the helpful suggestions.