[Absolem Jackdaw]

Nasty!
If you know a good welder I would'nt fret. looks repairable.
I'm more inclined to make you look for more rust spots and clean them first to make sure your frame hasnt been compromised in more then one spot, or like heavily heavily pitted.
That hole has been there for a while for the rust to get that far trough.
Inspect your entire frame thoroughly, preferably with some sanding paper or scotchbrite to remove rust to see clearly

 

[Absolem Jackdaw]

If there's too much rust / more i'd go find another frame...After that you are stuck with how to handle the new frame. You get it with papers, or get a clean frame and get your vin plate of (if it isnt stamped in) to switch it.
But that's for later. Wire brush and sandpaper sounds like a good start. Paint stripper sounds like overkill ? if the frame is rusted trough ,the paint will drop off. start with the spots where the rust comes trough the paint. Good luck ! Eager to see the report on the rest of the frame

 

[Absolem Jackdaw]

HI, me personally. I'd replace it. Living in Ohio all my life I found once you see rot through best to just replace it all . But welding might be a temp fix. Sorry old mans opinion.

Welders do tend to be expensive. Depending of the scale of how much you can DIY: fix is on one end, trash on the other.
I have a friend that works in metal and is a decent welder in training. If i'd took my rusted frame to her, it would be for a first opinion, and then to let her try a fix with option B still trashing the frame if the fix fails.
if you have to pay a welder to do that, its going to be an expensive option B ...