I would look at doing a butt for your first smoke. Butt is very forgiving and can be found around here anywhere between .99 lb to $1.89 lb. Go easy on the wood nothing worse than the bitter taste of an over smoked piece of meat.
Butt is cheap, and fairly easy. To really make it easy, get a dutch oven and do a Dr. Pepper Pulled pork recipe. Could be up for debate if it is BBQ or not though. But it is something I have found people who say they do not like BBQ that enjoy it. I usually toss it on the egg or the UDS.