Wow thanks for all your feedback. I have only been riding for two years but if I am understanding correctly my first investment should be the rear derailed and rear shifter.

I haven't changed these out before would it be worth paying a local shop or is it pretty easy to do?

Also the bike I got isn't complete 105 set-up it has the generic FSA 50/34 170 crank on it. Looks lie the 105 components are the shifters, rear derailer, front derailer, and casett.