These posts are a great place to start: start related topics at T-Shirt Forums
You'll find a lot of great posts about copyright, business licenses, the different printing methods, etc.
Your artwork is copyrighted as soon as you create it.
You can optionally register your artwork with the US Copyright office U.S. Copyright Office
You don't need a trademark to start selling t-shirts. You can optionally register one at the US Trademark office: Trademarks Home
Depending on where you live, you'll probably need a business license. If you google your city name and business license, you'll probably find your official local city government website with good info.
You may also need a reseller's permit to help log sales taxes within your state. This varies from state to state, so if you go to your state's official website and look up starting a business, you'll find all the info you need.
To do designs with a heat press, you'll probably want a quality heat press and then outsource the printing of your designs to a company that does "plastisol transfers
". That will give you the best quality transfers that you can easily apply at home. Trying to print them yourself with an inkjet printer probably won't give you the retail/clothing line quality that your customers will be expecting from your characters.