I am going to start working out at a gym, so what shoes should i buy running shoes or training shoes?

Either or: If you are working out at a gym, there is no reason to get fancy running shoes. I would suggest purchasing a pair of shoes that feels the best on your feet, whether they be running shoes or "cross trainers". If you plan on doing some running outside of the gym, the i would get the most comfortable running shoes you can find. I am a runner and asics are my favorites. Very comfortable!

Varies with activity: It depends on what you are doing in the gym. If you are weight-lifting and doing low-impact cardio (elliptical, biking), then cross-trainers are probably the best choice; but if running shoes feel more light-weight and comfortable, then go for these. If power walking/jogging at the gym, then definitely buy running shoes. You should be fit for either by purchasing at a quality athletic shoestore.