To start, you should get the book called "The ABCs of Reloading" and READ it. It'll provide you with a lot of useful information on safety, equipment, etc. After reading that book, it's time to go shopping for a press. You'll get a lot of varying info on what to buy, but for a new reloader, you might want to consider going with a single stage press (RCBS probbly makes the best one on the market today). It'll be easier to operate, and cheaper to get into. A progressive press will load ammo faster, but they cost more and are more complicated to operate when you are just getting started with loading.
Does nayone you know have a loading press? Another way to approach it is to get with someone in your area that can show you the ropes and even let you try loading some ammo on their press so you can find out if you like reloading.
Yes, you can load in your basement. The only thing to watch out for there is humidity to make sure your equipment doesn't rust. Location isn't as important as having a sturdy workbench.
Some people do seal their ammo, but I'm not sure it's really worth the hassle. Of course, I live in the desert, so moisture isn't an issue to me.