As above, get yourself to a running shop and have your gait measured and be prepared to increase your budget trying to find something that works comfortably for your feet.
I originally started running in some cheap £50 off-the-shelf running shoes (and yes, £50 is a cheap running shoe). There were ok for beginning running (i.e. C25K) but when I started to increase my distance I got pain and tightness in my right leg.
I had my gait measured, turns out I have a massive in-step on my right leg and I needed a pair of shoes to counteract / cushion that.