Here is what I have already
- power supply (400 Watts, few years old, I think I need a new more powerful one right?)
depends, what brand (make, model), if it is a reliable ATXv2.x+ / 80+ unit it should be just fine, most i3/7770 builds will never see over 200W from the wall IRL, and most PSU calcs put it less than 300W recommended. If you can post that or a pic of the label, that will let everyone know.
edit - here are a couple of good deals / examples of decent units for the price I have used recentlyAntec NEO ECO 400C 400W $40 + $5 shippingCORSAIR Builder Series CX430 430W $45 w/ $10 MIR
I would just go for the ASRock it's good enough and $10 less