My fav exercises are; pushups, situps, squats & pullups.
Pushups & pullups will do a lot for your upper body and there's plenty of variations to keep you from getting bored.
I pretty much only do the basic squats but every once in a while i'll lean against a wall and hold for as long as possible or do some lunges.
When i first started I aimed to do at least 100 pushups, situps & squats in a day so that might be a good starting point. Or, you can check out this site which aims to help you get to 100 consecutive pushups (instead of just 100 total). They also have a page for squats, situps & pullups and they offer a training program to follow.