Lots of good advice in this thread. The best advice, though, was the question of if you wanted a show-quality finish or just structural repair. Make sure you're true to your goals and follow the advice that comes closest to that goal.
My opinion is that first you have to prevent the rust spreading. I like a product called POR-15. Follow the directions, and when you're done the rusty area will be black.
The rest will be hard to describe without pictures, but I'll give it a shot.
If you THEN grind away the hole, it'll be a bigger hole for a short while, but you should see all shiny steel pretty soon. Try and open the hole up into a square, then cut a piece of steel a bit bigger than the hole. Use cardboard to create a pattern that is exactly like the hole you want to repair, then transfer that pattern with a Sharpie to your new steel.
Flange the metal, using either an attachment to your air hammer or a simple flanging Vise-Grip. The "embossed" or raised area of the steel should be exactly the same size & shape as your hole. The "lip" should be something like 1/8" -1/4" in several (if not all) places.
Now drill a small (1/8" or smaller) hole in the center of the new steel. Drive in a long sheet metal screw into this hole, but only about 1/4" - 1/2". Using the screw as a handle, insert the patch metal into the hole (sideways, crossways, or whatever works for you), then pull the patch metal until it fills the hole. Using your welder, put in a couple small tacks to hold it in place, then weld in the entire seam. A MIG welder with flux-core wire works really well for this in most conditions.
Remove the screw, weld up the little hole, then grind the welds until the whole area is nice and flat/flush. Repeat-weld as necessary to fill in the gaps, then when you're happy with the repair, treat the bare steel with your preferred Product (POR-15 works here too).
Then VIOLIN! Paint to match. If you do it right, nobody will know you did it and you won't be able to remember it had been done.