Never ever ever ride your bike on the sidewalk, exactly for the reasons Grant gave. Once you have better control then maybe in very rare circumstances, but still do your best to avoid it. If you aren't comfortable riding on the street yet, find a nice multi-use path to cruise around on or, worst-case, just ride around an empty parking lot for practice. Either will be much more safe than the sidewalk.
Definitely wear pads if it would make you more comfortable. They'll do a lot cut down on the cuts and scrapes.
Gloves are nice, but you should still learn not to stick your arms out when you fall. That's a good way to break bones once you get moving a little faster. Like Grant said, keep your hands on the bars and feet on the pedals when you fall. Practicing falling in the grass will help a lot with this, and it's pretty fun once you get into the swing of it.
It should go without saying, but make sure you wear a helmet. There's some debate whether they're helpful when you're out in traffic, but for the kind of riding you're doing (slow speed, good chance of falling without being hit by anything) there's no doubt that they lower the risk of injury.
Also, what a badass! Not many people have the guts to learn how to ride later in life. Congrats, and don't forget to have fun!
