should I finish all the other quests before I finish the main quest?
If you want to be able to do them, yes. New Vegas, as with non-DLC Fallout 3, finishes when you complete the main questline.
Besides, most of the fun of the game comes from exploring the whole of the Mojave and meeting its varied inhabitants
You could finish the main quest and then load your last save before completion and go around doing side quests.
You won't see all the endings unless you've completed all the side quests, but if you want to see the main ending you could finish the quest then go back and do all the side quests for the complete ending.