OK ... get the paint off of the frame choosing whatever method you select from the advice you been given. In this case it HAS to go down to bare metal so that no rust is left whatsoever. After it is painted — again whatever method you eventually choose — the BB threads should have that rust chased out. And the BB shell should be refaced. The tools involved are very expensive and there are skills needed to employ them. Thus you want to find a bicycle mechanic who knows what he/she is doing. A master machinist could probably do it, if he had the equivalent tools ... but virtually all of us rely on the bicycle specialists. The refacing ensures that the fresh paint/coating is not interfering with a precise parallel conjunction of the cups, spindle and bearings.
Here in Japan, I'm told that powder coating involves heating the frame and virtually blasting the paint off with heat. I don't know how that effects the rust, but they must get it out somehow. When I worked in automotive back in the Cretaceous, parts were sunk into a bath of caustic soda — as long as they were not aluminum. Anyway, who ever you send it to will give you the info.
However because you are stripping it yourself, I am assuming that you will be painting it yourself. In that case you must select a paint system of compatible undercoat and top coats. If I were to do it, I would choose enamels that I cannot get here in Japan — unless I am a pro. But in North America, you should be able to get industrial coatings from any paint shop that supplies the pros. These will be difficult to apply and will have to go on with the best brushes [sash tools] that you can buy. I am not going to go on and on about this — just follow me up. (At some time in my life I was a painter.) I do not think much of rattle cans, but polyurethane could do it fine, but with a lot of patience and nail-biting. Almost nothing is harder to paint than a bicycle or motorcycle frame — IMHO! Just my 2 cents.
Powder coating seems the best bang for the buck, but your stripping efforts may be wasted if the process includes ripping the material down to the bare surface as part of the service. I know what it is like to be on a budget, but professional coatings may be worth the sacrifices. It sure looks like a nice frame.