I'm using a HP Pavilion a6610t CTO
http://h10025.www1.hp.com/ewfrf/wc/product?cc=us&lc=en&dlc=en&product=3832268
And I'd like something new, should I get the 400$ one from the OP?
Hey, welcome. I used that machine before you as well, it's pretty good for 775!
It wouldn't really be worth it to get the $400 model as you wouldn't see much of an increase in performance. Plus, with the HP, you're running on the last generation Intel processors which really aren't that bad, and I wouldn't drop that for AMD.
If you're looking at doing an entirely new build, I'd recommend looking for just a case to start. Get yourself a larger, nicer chassis and put all the guts from the HP into the new chassis, and then over time you can upgrade everything piece by piece - starting with the HDD(s), then the Graphics Card, then the motherboard/processor/ram all in one show. Of course, you'll also want a good power supply.
That way, by the time your build is done, you'll have a really good system that you learned to put together yourself - you'll know how everything fits together and how everything is compatible and incompatible with the last generation architecture and the 1155 or 2011 architectures.