Every controllable business in the game comes under one of nine categories. If you own all businesses of one type then you own the crime ring.
Owning a crime ring comes with bonuses. The crime rings and bonuses are as follows:
Prostitution - The family gain knuckle dusters and inflict more hand-to-hand damage
Diamond Smuggling - Bulletproof vests that halve damage for both the family and your guards
Construction - Blown up businesses rebuild at double speed
Gambling - Double firearm damage with guns
Drugs - Drugs income doubles
Arms Smuggling - Carrying capacity for explosives doubled
Gun Running - Improved ammunition capacity
Chop Shops - Armoured cars become available at hideouts and Chop Shops
Adult Entertainment - Lower guard costs
You’ll own the prostitution crime ring early on in the game. Diamond smuggling is the next easiest as it is a small number of locations all in Florida.
After that I’d recommend drugs as it’s also easy to control and whichever other rings work best for you.