The simplest thing to do for bike shoes is go to a bike shop! Buy the cheapest stiff soled mountain bike shoes they have. Try to hold it to $80. You'll see shoes for $300. Cheap shoes are a good start, though. If the bike shop doesn't have cheap shoes, try on some and find out what your size is. Then order cheap shoes from Performance Bike or Bike Nashbar online.
Bring the bike with you or ride. Ask the bike shop if they have toe clips that will work with your pedals.
The WalMart bike will be fine for a long time. You're not trying to set any speed records, just to have fun. It's amazing how much fun it can be to just go somewhere on a bike. So do that. Explore roads and streets you've never driven on.
Losing weight is all about both diet and exercise. Don't starve yourself, but you will have to feel hungry some. Don't ride too slowly. Do push it a little bit. You want to sweat and breathe deeply while you're riding. Work done equals calories burned.