Good topic, I'd like to add in my experiences:
1. The taxi mission glitch is the best way to get in. Just push L3 one second before you bust through the gate. You earn a good 10-20 seconds of freedom depending on who sees you.
2. The military AI is pretty dumb. The "canal" or "ditch" along the perimeter is the best way to lose your wanted stars. I like to drive to the western end of the runway to attract the soldiers, then speed down the runway to the fence opening just past the fire trucks on the right. Hug the inside wall and drive around the corner until they lose sight of you, then just sit there. They will drive around and look right at you but do nothing. Except for the soldiers on foot. They will spot you through the fence or walk down the canal. The best way to get rid of them is to take another loop around the base and let them despawn.
Once your stars are gone you can switch characters. I discovered that after running a mission with a different character and saving, then switching back, the character left in the base will exit on his own in the vehicle you left him in. That is how I got a Humvee and Minigun for Franklin.
3. Lazer - The easiest one to get. I just pulled up next to one in the carport hangars with the taxi glitch and hopped right in and took it to Trevor's hangar. I used the low flying technique to avoid the missiles, then went high above the helicopters.
4. Titan - I have yet to get one off the ground. I will try the idea of stealing the one on the runway.
5. Buzzard - There is one on top of the government buildings on the southeast end of the map. Much easier to get with no stars. Just climb any ladder and you'll get there eventually. I do have it stored at Trevor's helipad.
6. Rhino - I was fortunate at one point to have a saved game where the Rhino spawned right at the front entrance and headed toward the tower every time. I used the taxi glitch and Franklin's ability to get next to it. You'll want to turn off his ability when you are slightly behind it and to the left - this will cause the turret to slowly turn to the side, then you can park in front, get out and throw the soldier out, before it turns around and blasts your taxi.
So far, the canal will not work to lose your stars, because every time I'm in a tank, they call out the helicopters immediately. The key to escaping is to go out the east gate and head for the nearest railroad track. As mentioned before, every car you hit with your turret has a secondary explosion that will do some damage, so the best thing to do is avoid collisions and never target anything up close. Once you're on the tracks, head for the nearest subway tunnel. That is the only way I have found to lose the choppers. Unfortunately, I'm only 12% through the game and have nowhere to store the tank.
7. Cargo Bob - The chopper that flies a pattern around the fort is, in fact, on the ground for a very short period of time, as proven with the photos previously. I have stolen it once, almost by accident, as the pilot had bailed and left it on the helipad. However, it did not survive the onslaught from the pursuing helicopters. I tried to land to draw their fire to me, but it was destroyed on the hillside next to the fort.
I was able to replicate the scenario for the pilot to bail, but have not been able to fly it again. It pretty much spawns with rotors spinning ready to take off. To make it spawn, I drove around to the truck parking lot on the west side and then headed straight for the helipad. Once it appears, you have to hit it with a few rounds shooting out of your car. When it spawns there is usually still a fence between you, so just fire blindly in its direction. Once it is empty, and you are near it, any tanks in the area will destroy it, and if you look away for too long or stray too far, it will sometimes disappear. It is definitely the most difficult to steal.
8. Barracks - This one can be tricky, I think it may be more luck of which cops spawn where. There is no hiding this one to avoid stars. I do prefer to lose my stars, get a good position on one near the eastern helipads, and then use the taxi glitch to get out in the open. Leaving the fort is not difficult, and I have a repeatable strategy for losing the cops once outside.
Leave out of the eastern gate and immediately turn up the hill on the left before the bridge. That dirt road leads to a loop at the back of the water treatment area. Head for that loop but stay off the dirt road, I drive straight north. Once even with the loop, you will see a washed out gulley area on the hillside on your right. Drive up as far as you can, and hit the emergency brake and sit there. With any luck, you should be out of sight (turn off your headlights), and they'll drive right by and not see you. Unfortunately I have nowhere to store it again.
9. Humvee - I forget the game name, and it's more of a jeep I guess. This one you can use the canal to lose your wanted level and switch characters. I did it with Franklin and he ended up at the rec center in LS and the jeep was parked in front.
10. Minigun - I have gotten it with Franklin and Trevor in one play without technically dying, although I died many times in the process of getting to that point. The important part is reaching the inside stairs of the control tower with as much armor as you can. There is a soldier on the 6th level who may be out near the stairs or in the room on the left, sitting down. There are usually two in the top room of the tower. I use a grenade launcher for them. The entrance and exit are the tricky parts.
Franklin - Entrance - Use the taxi glitch and his ability to run over the guard in front of the tower and hit the front door with the taxi to make it open, this usually encourages the 2-3 soldiers in the lobby to come out after you, and you don't walk in blindly. (Funny story: one time there were 3 prostitutes in the lobby and no soldiers)
Exit - I like to take cover behind the desk in the lobby and fight it out with the soldiers who come through the door to raise my ability bar. Once full, I sprint out the door and run to the right towards the fenced gate. The left side of the fence is a swinging gate when you run through it. Directly on your left is a storage silo with a ladder. I like to climb it, then jump on the roof of the warehouse, take out some soldiers in jeeps, and when the opportunity presents itself, jump down and take off in an empty jeep. I'd recommend just going straight forwards or in reverse in the opposite direction with a little bob and weave as fast as possible. Fancy driving or trying to turn around will get you picked off by a tank. Head for the same canal opening by the fire trucks and hit Franklin's ability when close and use it to hide down the canal.
Trevor - Entrance - Use the taxi glitch and hope that a tank is not right next to the entrance. Run over the guard and activate his ability as soon as you get out. Trevor can waltz right into the lobby with guns blazing, but turn it off as soon as you can to conserve.
Exit - Fight some more to raise the ability bar. With the ability activated, run right through the same gate as before. This time keep running straight towards the runway, hang a left and there should be a vehicle parked by some containers. Again no fancy driving, just steal it and go. Steal a jeep once your in the open later on to lose your stars, then switch characters.
Michael - Entrance - Use the same technique as Franklin, drawing out the soldiers.
Exit - Same technique as Franklin. Once on the roof of the warehouse, use his ability to take out the soldiers quicker before reinforcements arrive. I would have had this one except a strange thing happened: the guard at the east gate left his post to go snooping around the outside of the perimeter fence. I could not go anywhere to get rid of my stars and I could not see him to kill him.
11. Leaving the base with no wanted level - It is possible, with a little finesse. Proceed to lose your stars in the canal as stated previously. Now head toward the east gate through the canal. After that final turn, stop next to the inside wall. You are going to get out, take out the gate guard with a silenced sniper rifle, and then drive back into the canal as far as you can next to the fire trucks. As long as no one saw you, you should have just 3 stars. Let those pass and you should be able to go down to the gate without being seen. Pull up next to the concrete building at the end of the canal, jump from the roof of the car to the roof of the building, then drop down to the right to be home free.