From my experience as a LR Defender owner (known for chassis rusting):
- Rust, once there, can spread. It will not go away. So if you just take it out on sunny days you will not be making it get any better. Sometime or other you will need to get to grips with this rust problem.
- From what can be seen in the pictures, the muffler seems OK. That's a good start, since this part can be costly for some makes of car, specifically those that weren't produced on a very large scale such as yours.
- On the other hand, some of the suspension struts seems in a pretty bad way. At the very least, you will have a bad day whenever you will need to take a brake pad off - or, even worse, renew a gaiter on the transmission.
I recently had my truck over to a paint shop to get the transmission scraped and repainted (with black chassis paint). This didn't cost more than $300 equivalent, so I guess will be a good investment to preserve the vehicle. They had the skills, tools and products needed to do a professional job, I didn't.
Even if you intend to keep the car for a short period of time, I would go ahead and have it done professionaly since the first thing a potential buyer will do will be to have a look at the underside.
Additional note: was this rust caused by road salt, by any chance? If so, take a close look at any rubber parts (bushes, gaiters) underneath, they can get dry and split due to the action of salt.