> Do I need an air pump? If so, what is recommended?
I would say yes I liked the stone ones because it gives a nice "wall" of bubbles while putt air into the water.
>Is there a preference between silk and plastic plants?
None in my personal opinion, but maybe someone else has something to say
>How much gravel do I need on the bottom?
Maybe 1/2 inch; enough to cover the bottom.
> What can I put around my heater to prevent my fish getting burned, that also looks attractive? Rocks, tank decorations, etc. The only way fish will be burned is if its TOO hot. For most 0 - 80 degree tanks I've never really had a problem with fish being burned. But maybe towards the bottom but DO NOT cover it with gravel.
>Is an undergravel filter necessary?
NO and I don't recommend them, either. They just suck everything to the bottom and while in theory it sounds good, it makes your tank LOOK clean but everything is hidden by the gravel.
>Is there anything else, equipment wise, that I need?
Just a heater, depending on what type of fish you have, a filter (MUST have) and an air pump!

Also keep in mind that the rule of thumb as to the AMOUNT of fish you can have in any given tank is 1 inch of ADULT fish per gallon. So lets SAY a fish you choose right now is only 1/2 inch but as an adult it will be 1 1/2 inches. That doesn't mean you can buy 20 of them!! It means that you should NOT have any more than 6 of them together in a 10 gallon tank.

Hope this helps!