Running shoes?

So my winter training plan is going to include a lot of running for aerobic fitness. I found last winter that I can run in temperatures much lower than I can bike in, and it's pretty convenient and inexpensive versus buying gym memberships, rollerblading, etc. So far I haven't contemplated anything over 5K, so the older but lightly used Avia cross training shoes seem to be adequate. I have to wonder if it's a good idea, though, being a running newb. Being several years old, but only using them for actual running (i.e. not wearing them as street shoes), I'd suspect they haven't "broken down" yet, but I hear runners replace their shoes every few months to a year. Also being "cross trainers" (I believe), am I potentially increasing my risk of injury by using them as running shoes? Does it really matter what shoes I wear if I'm just running around Lake Harriet or Calhoun? Even though I only run 3-4 miles, does the frequency make a difference (two maybe three times a week)? If I do need new shoes do I have to spend lots of money on them to get a decent running shoe? So far I haven't felt too much pain after running (after the initial couple of runs of course!).