Back in the seventies, I had a small area of bubbling on the lower rear corner of the passenger door of my 65 Barracuda. I had very few tools then, but I used some kind of attachment on an electric drill to grind down the outside, then, with the door panel off, of course, I used a screw driver to reach down into this dirt trap of an area between the outer door skin and the inner panel. Scraped it clean as best as I could, then sprayed carb cleaner into the area, then squirted motor oil into it, then finished it off with spray undercoating. Little bondo on the outside, sand it smooth, paint.
Fifty years later, that rust still has not returned.
Barbee, southern cars rust from the inside, northern cars rust from the underside from the salt on the road. And, in response to another's suggestion, unless you're right on the beach, a nearby ocean won't hurt.
Trapped moisture is a rust breeding ground. And dirt traps moisture. Moisture that seeps in from around the windshield or weatherstripping and gets into carpet doesn't dry out. Moisture that gets into an area between two sheet metal panels with dirt in them that can't get out stays moist. Best rust preventative is clean and dry.
I've got a 64 Polara convertible whose interior and trunk floors have numerous perforations from having been parked out in the weather before I got it 30 years ago. I think the trunk floor got sandblasted years ago, but the interior floors have never gotten any prep. It's been garage kept since I've had it. The rust is no worse now than it was when I got it. It has new carpet in the interior, so looks great. Because it's a southern car and has never been driven on salted roads, the frame rails, rockers, quarters, fenders, etc are all solid as a rock, so it's perfectly safe to drive. Now, if I was actually going to restore it, I would replace the interior and trunk floors. But for a driver, I'm just not going to spend the money.
Again, clean and dry. If the OP's car is parked out in the weather, he could spend $$$$ to really fix the floors right, and still have problems a few years from now for the same reasons the floors got rusty in the first place. And I know everyone doesn't have a garage - I didn't until I was in my thirties. But it's a reality that cars that sit outside in the weather will deteriorate.
So, you pays your money and you takes your choice. For a 64 Valiant driver that sits outside, I wouldn't spend the money to weld in new floors. Take a less expensive, easier way out. You can still replace the floors later if you really get compulsive about it.