I'm not too sure about plant types, but try going to your local fish store and ask them. It depends on the tank size and lighting, really. Most plants sold at fish stores aren't too hard to care for.
I think that the less chemicals, the better. Try using a large flourescent bulb (12T+) that's at 6500 degrees K. This helps grow your plants without too much algae growth.
I put some tetras or rasboras in a planted tank. They school and look very nice around the plants. Most livebearers like platys and mollys won't eat your plants. Many chilids like to eat plants. Normally, it's the larger fish you should stay away from in a planted tank. I'd say nothing over 3".
Oh! And I wouldn't worry about algae growth too much. Many newbies to planted tanks freak out when they get algae. A little algae on your plants will actually make your tank look nice. Be sure to scrape it off the front of the tank so you can see. I'm not saying to do anything to encourage algae growth, but having some doesn't hurt. If you start getting blankets of it everywhere, then you should get an algae remover that's plant safe. It's very important to check that it is plant safe, because some WILL kill plants! Even plant-safe will do a little damage to them, so don't use algae killer unless it's an emergency.
Hope this helps!