Getting into pc gaming

HI im trying to get back into pc gaming and I have no idea what to do I have a old inspirion 530s I used to use but I would need to upgrade almost everything in it or should I build my own custom rig or I was thinking about buying a prebuilt and just having to upgrade the graphics card on it what would be my best bet to do and also with mice and keyboards and speakers keep my old cheap ones or should I upgrade them too. I would just like to know what would be my best bet would be to save money and also I want to play games like skyrim and crisis and even older games like doom 3 and play newer games when they come out. and on the 600 dollar build on the tek syndicate youtube channel the sapphire radeon 7870 is going for 220$ and up so any advice on other cards I should purchase I want to spend about 150-200 in a card yet or I was looking at this card http://www.amazon.com/Sapphire-version-PCI-Express-Graphics-11217-04-20G/dp/B00FLMKN6I/ref=sr_1_2?ie=UTF8&qid=1391125030&sr=8-2&keywords=sapphire+radeon and I would be willing to spend the extra cash if its any good I plan to not have to upgrade this pc for about 5 years so I want it too last.

It might have been said somewhere, but what would be your budget?

 

Also I wouldn't recommend buying a prebuilt and throwing a GPU in there as the PSU will probably be the bare minimum to save money. (Most Dells ship with 250W and "gaming PC" makers use the 500W ones that come with their shitty flashy $30 case)

My budget is about 700 to 800

http://pcpartpicker.com/p/2KBrL