Ok, I'll have a go. This is my opinion only, and evryone else might disagree, so do have some salt to go with it!
I see what you mean about the patch welding: it's not the prettiest, but I
have seen worse. As long as you knew about it when you bought the van it wouldn't worry me too much.
The garage who did the welding have sprayed schutz - a type of underseal - over their work. That's fairly common with MoT work, in my experience. I never liked garages using the stuff on my cars, but it's hard to stop them if you don't do the welding yourself. All it does is cover up rust and make the area look OK for a few months, as you've discovered...
So what to do? Well, is that your lift that the van is on in the photos? If so, then here's what I'd do:
1. Go over the rusty bits on the underside with a wire brush, preferably one mounted on a grinder
2. Clear as much loose stuff off as possible, as well as flaky areas of schutz
3. Steer clear of more underseal type gunk - unless you're starting with rustfree metal or paint I've always found that rust festers worse than ever under the underseal
4. Mix 50/50 waxoyl and old engine oil, and pressure spray the mixture at everything in sight under the van, as well as in all the cavities and box sections
5. Repeat step 4 every year or two!
If you don't have a lift then all the above is harder but not impossible: ramps are your friend in that case.
So, dog or puppy? I'd say neither. As long as you can accept your van will never be 'concours' then I think plenty of Step 4 will keep the rust at bay and let you enjoy plenty of bongoing.
What are the back wheel arches like?
