Re: running shoes
A decent pair of running shoes vary in costs, but you shouldn't be paying more than $60 TBH
IMO, cheaper might actually be better. Don't get it too clunky, get something that allows you to actually feel the ground underneath your feet and have some semblance of toe gripping. It will teach you how to run correctly, and save you heartache and other aches in the long run. And don't replace as often as they say-really, the shoe should just be something to protect your feet from glass/bacteria as you let your body do the rest of the work.
This is coming from a runner with extremely flat, almost nonexistent arches. Initially, I bought
into the running shoe buying and replacing recommendations hook, line, and sinker. I gradually developed more and more aches and pains-including back, hips, knees, and could run less and less. Finally, I decided to throw out my orthodic inserts, and use a cheaper pair of my cross trainers. I taught myself barefoot running technique-just mimicked it as much as possible with shoes on. Its not perfect, but my hip problems which I've tried tons of stuff to fix are now gone.
Re: other gear
IMO gyms are a good investment. Like a friend said, I think a gym could be a motivating environment-once you get there and plunk yourself into the middle of all these exercising people, you feel weird to just stand there. You end up getting moving in some way or another. Unless you're a very self conscious person, then working out at home might be better.
Speed rope (I love jump roping, regular jump ropes aren't suitable for exercising...at least not for me).
Regular ropes are flimsy! It might be because I'm really tall and regular ropes...never are even the right length, but I have one of these too and its very useful for a quick tough workout.