Don't worry about the "Near Miss." This is just a stunt, like a jump or two wheels - I think it just triggers when you pass a vehicle very closely.
I just stole my first AmmuNation van today. To steal one, first pin it up against a wall using another vehicle. Get out, walk a safe distance away, and throw a Molotov cocktail at it. The driver, passenger, or both will get out of the vehicle. At this point, you should run a safe distance away, for two reasons:
1. You will have one star from throwing the cocktail, and staying too close to the vehicle might cause a cop to catch on fire and you'll need to deal with a two star wanted level. 2. The occupants of the AmmuNation vehicle have shotguns. Those hurt.
When you feel comfortable, head back and steal the AmmuNation vehicle.
I don't see the point in stealing the gang vans - I'm making so much money through regular trading that it doesn't seem worth the hassle. And I'm not really trying hard - just buying and selling things that the game says are a good deal, and trying to make sure I get to the guys who email me.
Stealing gang vans comes in handy after a while. Sometimes you'll be stealing drugs which you don't have a good buyer for, but once someone hits you up for that particular drug, you'll already have a stash of it.
Just shoot the Aummu-Nation van 3 times with a regular shotgun. Once the driver gets out, knock him down quickly with a flying kick. Finish him with a melee weapon (chainsaw or sword) or by punching him. You can dodge bullets using the "vault" button. The one you use to jump over walls with.
It takes: 3 regular shotgun shells 2 sawed-off shotgun shells ~full clip of a micro smg 23 rounds of a regular smg 23 rounds from regular or double pistol ~2 or 3 rounds from revolver.