I'm currently building my very first custom PC and it is a Mini ITX as well. I'm needing some help from the experts because I've trolling YouTube and Google trying to find answers but everything I find is outdated or un-related.
I'm going to be using this PC for normal day to day use (internet, office, etc) along with gaming here and there. I'm on a budget but also wanting something that will perform well and last awhile.
I understand the basic differences (i3 hyper-threads w/o tubro & i5 turbo w/o hyper-threads - essentially the same amount of processing ability...just speed differences). So I'm stuck since I've never seen anyone with less than an i7 where I'm at but they do hardcore editing or gaming so I don't need what they need.
I highly recommend the 7770 over the 550Ti. The i5 is a quad core w/turbo and the i3 is a dual core with hyperthreading but w/o turbo. While there aren't a ton of games out in which a quad core makes a huge difference there are some (BF3 multiplayer for instance).
An i7 will almost never be a better choice over an an i5 in regards to gaming performance relative to the cost difference between the two.
My recommendation would be to go with the i5 and the 7770 if you can afford it now as that combination should have a much longer gaming lifespan and best upgrade path over the i3/550Ti or i3/7770 combo. You would likely only want to upgrade your video card in two years for example, whereas with the i3 you would be looking at a processor and gpu upgrade in two years (assuming you are trying to keep up with current releases).