ok, firstly.. What was your old pc? (what Processor?) because for all we know you had a decent quad core and only need a new psu and more ram..
Second.. the amount your spending on processor and motherboard etc should go into a new GPU..
The biggest difference you will see in any game will come from a better GPU(until it's better than your screen)
My opinion is that if you have a 560 ti in your machine then it's not THAT old and you may only need a couple of upgrades if it's not totally dead.
If it is dead, then I would suggest the cheapest of an i5 2500k with at z68 board OR an i5 3570k with a z77 board.
A CM 212+ for a heatsink.
8GB ram (2x4GB 1600Mhz)
1TB HDD of your choice (I'm a W&D fan.. Black drives are good)
Corsair, xfx, Antec branded 650 Watt PSU
A Nice case, I really like the
Corsair Graphite Series 600T Special Edition White Review but it is expensive and there are very good cheaper options (cm haf 912 etc)
Finally.. a GTX 670.. (this will last you a few years and to really get the absolute best out of it you would need a better monitor.. So you know it's gonna last longer than your monitor is..)
That should come to roughly 1200.. maybe a little over but price-match and catch sales and you'll get it..
Although many rant and rave about how fast a SSD makes their system.. if your gaming then you won't see any gain EXCEPT load times will half(depending on what it is..) for windows, games apps etc..
While your in a game you will load it fast.. and then nothing.. The GPU will make more difference more of the time in almost any newer game and is in my opinion the better investment..
Again I would put a decent screen above an SSD.. you look at it so much it may as well bet a good one.