When should I start adding people to my mafia? Should I avoid having a big mafia early on?

Start adding people right away. Get to 501 mafia as soon as you possibly can. There's no downside to having a large mafia, even if it's not fully equipped. An unequipped mafia may not be helping you win fights, but they won't be causing you to lose fights necessarily either. In fact, having a large mafia during even the earliest levels has outstanding benefits:

1. More people in your family helps you purchase Mafia Mike's properties which are 1) cheap, 2) earn decent income and 3) cannot be robbed.
2. You will also be able to purchase plenty of Limited Edition Loot (usually just $10000.) You never know when something amazing will be offered. They rarely stick around more than a few days so you don't want to be left scrambling for mafia members to buy what you like.
3. You earn 3 experience every time you fight as one of your family's capo -- the larger your mafia, the more often you'll see you've fought as a capo & get passive experience!
4. You'll be able to put together a good Top Mafia early on -- the Mastermind position (which can give up to 11% more experience per job) and the Wheelman position (as much as 11% less energy needed per job) are particularly beneficial.

Once you've got 501 people in your mafia, you can feel free to continue adding people for all of the above reasons as well.

For information on how to get a larger mafia, see this FAQ.