In v 1.4 of Mission Maker - possibility of dressing up CJ (a.k.a Clothes Shops) were added. Now you can enter any Clothes Shop around San Andreas and buy clothes for CJ, then save it and make it appear in the mission.
How to do that?
1. Head into any shop (as previously said) - you have 999999$ so you can buy anything
2. After you dress up CJ - open up MM menu and Player Settings > Save Clothes
3. And then make mission with CJ character. Clothes will be saved & they'll be visible in the mission!
How about barbers? - Barbers aren't enabled, HOWEVER you can actually use a mod menu to change CJ appearance completely and when you click "Save Clothes" it will also work, so basically you can change hair, beard, add tattoos from the mod menu.
How about Tuning Shops (car tuning shops)? - They're also enabled (from version 1.4) make sure you see the red wrench icon on the map > Go there with any car (of course remember, that these shops might be only for Lowriders, or Fast, Normal cars) and tune your car. You need to do it before placing the car, so better thing to do is to start your mission near the tuning shop - because otherwise you'll be far away (or just use airbreak mod to fly there instead). Then place the car - and car will be modded.