the 1090T is still fine for gaming, it's a 6 core with more performance per clock than an fx 6300 (albeit without hyper-threading), so it's still strong for a year or 2, just focus on a new GPU because that HD 5750 is old and a new one you benefit you the MOST out of any other single component in your system, go for something like:
HD 7870 Tahiti LE
http://www.newegg.com/Product/Product.aspx?Item=N82E16814131484&Tpk=7870%20tahiti
biggest bang for buck you'll ever get out of a GPU, you pay $140 after MIR for the performance of $200+, can run modern games just fine on 1080p (high settings or tweaked ultra completely possible) at high frame rates
HD 7950
http://www.newegg.com/Product/Product.aspx?Item=N82E16814161420
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202026
another big performance/price card, both of the above options are great, fits your 250 budget snugly
or one of the new R9 270x's
http://www.newegg.com/Product/Product.aspx?Item=N82E16814202050
the above is fine or you can get a factory OC'd one for slightly higher performance (will usually be the more expensive cards like at 229.99, they will either come with better coolers, a factory OC, or both)
again, do not replace your CPU, it is completely fine and would actually still be a recommended buy for a budget gaming CPU to this day if not for the fact that the Thubans have been out of production. If you have doubts then buy an after market cooler along with a new GPU and give it a good 0.5 Ghz overclock. Trust me the Thubans are better than people give them credit for, switching to an FX would be more lateral movement (or even a downgrade in terms of single core performance) than an upgrade.
And of course upgrading to an i5 3570k would be ideal, since it is the sweet spot for gaming after all, hefty core performance with good overclocking ability. But considering your budget, a new GPU would be best.
Your RAM could use a slight upgrade but that can wait, 6Gb is still fine today, but perhaps you should look into a nice 8Gb 1600MHz kit or something similar in a year or 2