There are pretty much as many different types of training shoe as there are person, so it’s almost impossible to advise which shoes you should buy.
If you go to a running shoes shop they often have the kit to allow the shoe-seller to look at your running style (gait) in slow motion and give you some advice about which shoes might help you to run better; they may even claim to be able to prevent injuries. Some places offer moulded insoles. Many runners are very happy with these services, but I would advise a little caution. How much running do you do on a treadmill when you’re wearing jeans and how different does that running ‘feel’ from your usual running? Is the person trying to sell you some shoes getting a realistic insight into your running style?
Equally, if you’re comfortable in the shoes you’ve got (which may well be cheap as chips), and don’t suffer from any soreness in your legs, there’s probably no need to change. If, however, your toes, ankles or lower legs (especially) are sore, it might be time to look at something different. Shin splints (a horrible, stabbing pain in the front of the lower leg) can be a sign that your trainers have lost their bounce, but that’s not a medical diagnosis!
Most of all, you should feel comfortable in your shoes. Experiment with tightening the laces in different ways and find out what works for you.