Specifically:
-Up to 1 weapon
-Up to 1 armor
-Up to 2 items (These items cannot be a weapon or armor and must be usable during a crime. For example, a car may be usable if it is available to you. Also, you cannot use the same item at the same time with a mobster you own.)
You have to choose what to take with you wisely. You may receive a penalty if you use something that is unnecessary.
For example, carrying your bazooka in the bus while trying to steal that wallet isn't the best of ideas. Use common sense.
Ultimately, there will be crimes that will be impossible to do unless you take along specific items. (For example, if you are stealing gold bars from a bank, you need a large vehicle to help you move them.)