I have been to the Sheriiff and he teells me I can't have the supplies until I am armed. I have been to Rusty's several times but have yet to have him offer me any miniguns. I have bought soe parts from Rusty, bombs and a hover something, but they don't matter to the Sheriff and I can't get to the third race without mini guns either.
You know what maybe you already have them and you need to activate them. Go to the shop and click on tune for the car you want to tune. From there you'll see suspension, boost, tires etc. Weapons will be one of them, just install.
Also you may have them installed already but in order to use them you have to buy ammo from a vendor. I think every vendor sells the ammo. It's like 20 or 30 bucks for 200 rounds. Buy alot because you'll need, 200 rounds goes fast.
Edit: you can also edit your vehicle when you exit wellsprings. At the front of wellsprings is a garage with little dude in it or you can just exit the normal way.
After reading everything you've said I'm almost positive you don't have any ammo for you guns. If this doesn't work then I'm not sure what to tell you. I have the guide book but only for collector purposes. I really would like to avoid opening it up, at least till I'm finished.