Also, an extra sort of question, does all the wiring needed come with the hardware and/or the case, or is their some extras that I need to order? If so, please list which ones. Lastly, (as an extra question), how do I get the power button working, the 2 USB ports, and the sound/audio found on the front of the case?
Compatible, yes. Something you should buy, definitely not.
Do you have a budget? I can give you some tips on how to make this better.
1) Dump the 550Ti. Its a pretty terrible gaming card. Its old, uses alot of power, and is not very fast for the price.
2) You do not need a Z77 motherboard for your processor. You can use a H67 motherboard.
3) That being said, I would go with a H77 motherboard and a second generation Intel i3.
4) Pick a power supply of a brand Antec, Corsair, or Seasonic. They are much more reliable than the CoolerMaster you chose.
Can you possibly give me a link for the graphics card you recommended and the power supply, please? Also, I plan on actually updating the processor in the future when I save up some money, if that makes it any more reasonable to keep in the setup. But for certain purposes, if it is possible that you can post some links on the components too, that'd be great.