Well, my own history is a bit checkered, but about 70 lbs. ago I ran my 13th and last marathon. Something like 250 20 kilometer runs and God-knows-how-many-other training miles in shorter distances are in my distant past.
My knees are trashed, which makes low impact (translation - elliptical or swimming) the best way for me to get the cardio in.
So I have a ton of experience with shoes. What Thor, et. al. says rings true -- although you have to pay attention to foot width. As I generally buy two pairs of shoes and throw them away, wearing the boxes they came in, my feet are wide. New Balance does real well with wider feet, but I've had great shoes with Nike as well. BUT, there's no need to get real expensive shoes. Just some comfortable walking shoes are fine. If you have wide feet like I do, forget about Foot Locker or any other shoe source in a mall. You really can't get anything wider than a D, and when you wear EEE like I do, I have to go online. Zappo's works real well for that, though they can be pricy sometimes.
If you're going to get some pool time in (this is the real fat-burner for me), you should get yourself a pair of swim goggles and a pair of ear plugs. Chlorine in the eyes after a while makes you look like a druggie.....oh, wait.

And water in the ears transfers directly to water on the brain, which is not good.
By all accounts, slow and easy is the way to go. None of this is a race -- you're simply trying for a measure of fitness and you have the rest of your life to find that measure.I've talked a little about exercise and dieting in another thread -- "17-Day Diet" which is in the Lounge. I've been on this thing for about 7 weeks now and have lost 29 lbs., 4 inches on my waistline, and feel much better than I have in years. So the low-fat, low carb thing works, and now that I have a dog that's 30 lbs. overweight, both she and I are doing double sessions daily. She gets on the treadmill and I'm right next to her on the elliptical. The pounds are melting off.
I have a weight machine, but I ain't using it right now. All available time is spent doing cardio. I'll eventually cut back a little on the cardio and pick up weight training (using a machine rather than free weights), but not for awhile. I want to lose another 20 lbs. before I get into that.
I didn't know about the pool temps being too cool -- I learned something today. Thanks, Thor.