@dankdogejust to chime in on this - if you want to keep your existing Motherboard for ease - an I7 2700k or I7-3770k is the best cpu you can fit in the 1155 socket, the 2700k has the best Single-Thread-Performance rating and is a drop-in replacement.
A I5-2500k is also the same socket and a bit cheaper than the other two mentioned above. Any 'K' series intel processer has what's called an 'unlocked multiplier' which means you can easily overlcok the CPU by increasing the core multiplier count, provided your motherboard supports the feature.
If you are upgrading to a new CPU+Mobo, you might as well get a 6600k or 6700k as these are the latest series and will (in theory) last you longer than a 2xxx, 3xxx, or 4xxx series, though I have a 4790k myself and it's a good strong CPU.
As for the difference between motherboards which cost $40 to those that cost $100, there isn't a HUGE amount of difference, it's mostly on some features such as Available outputs on the back plate, number of PCI-E slots (for GFX cards etc). I.e. some higher-end boards will have more outputs, maybe built in wifi etc. Some bigger ones will support 3 or 4 GFX cards etc.
Basically pick a board with the same Socket as the CPU you want to use, ensure it has 1 PCI-E slot for your graphics card (a 960 uses PCI-E 3.0, but is backwards compatible with others) and you're more of less good to go. The 6600k/6700k cpus use DDR4 memory so you'll need new memory if you go that route.
Almost all (99%) of motherboards available use the 'ATX' standard to define their size, and pretty much all PC cases are 'ATX' compatible. The majority of consumer motherboards are usually the same size, and your PC case should have pre-fitted holes that it will line up with. I suggest you watch a couple of PC building videos on youtube, this will give you an idea. It's not difficult, but can be a tiny bit scary if it's not something you've done often.