Well lets see, if you are really limited you may want to consider going with an APU. The a10-6800k for example. It won't do as well as the 7770 or the FX-6100 but it will perform very well. You can play all the modern games on it though at lower settings sometimes. The biggest plus to it is you can get your entire system counting CPU, GPU, Motherboard, RAM, Case, PSU, HDD, DVD Drive, Mouse, and Keyboard all for under $350. Would perform really well.
The second best idea I would recommend for you if you are planning to upgrade this in a little while would be to get a better graphics card and a worse CPU. For around $150 you could get an AMD Radeon 7850. If you want a good step up you can go for an AMD Radeon 7870 GHz Edition for close to $200. That would way outperform the 7770. After you do that I would say get an AM3+ motherboard and the absolute cheapest CPU for it which is around $50. After that wait until around December/Janruary when AMD will release the new Steamroller based CPU's and get the newest and best FX 8 core CPU probably for about $220.
Going this route you will have an alright system if a little slow at times until December but it will still be able to play all of your games without an issue, and when the time comes you will have that new CPU and it will way outperform the 7770 and FX-6100 combination by a long shot. You will save money in the long run too since you won't have as much invested in parts you will replace.
If you do not want to go either way I can search and put you together a system for around $400 and send you the links to all the stuff.