If you're hiking on mountain trails, and you don't say if you are, hiking boots are made for that. Today's light-weight hiking boots are really running shoes inside a firm support shoe for the bends and creases of mountain hiking. Aside from that, if you don't have shin splits -- if you do, you have to deal with that before doing anything else -- are you stretching at all? You might be very tight, which makes it harder to do new things. The other thing about mountain hiking is, when people are new to that they usually work their mileage up slowly before tackling long hikes. Jogging can help with this. So can sports like basketball and football and soccer, as they get you're legs used to moving for a long time in difficult conditions. At the gym, the treadmills should elevate so you can slowly break yourself in to this new activity -- again, assuming you don't have shin splits, which usually come from running on hard surfaces. And yes, if you have old shoes, they will hurt you. If you go to an outdoor store, look at the running shoes they sell for mountains -- they're light, but much more supportive than regular running shoes.
I suggest seeing your doctor first! If you have flat feet that could also be a problem that causes shin splints.
You should also wear GOOD FITTING ATHLETIC WALKING SHOES!
As I said see your Dr. first to get a diagnosis! If it is shin splints then after treatment is completed then start a
strength-training program for the lower legs. That will help to take pressure off of the soft tissues.