Foxes can bite through cheap chicken wire and will also try and dig in, rats tend to burrow and are near impossible to keep out with mesh alone.
I would say buy the best mesh you can afford for the walls of the run, especially the bottom section. You could get cheaper stuff for the upper parts of the walls and roof. If you make a shallow trench along the run edges, lay in a stretch of mesh or chicken wire and backfill over it, that also helps. If a fox starts digging and hits mesh, they tend to give up. You could also use a more solid type of run wall for some sections. It gives the birds some weather protection, so you could have a timber wall on a couple of sides for the bottom at least.
Bird flu is becoming more and more frequent, so a roofed run is well worth investing in. Mine is roofed with chicken wire and covered with plastic roofing sheets.
Treadle feeders do help prevent food spills and that helps prevent rats. A galvanised dustbin makes a cheap and effective food store. Bags of feed just call out to rats. The thing is with rats is that they are always with you, whether you see them or not. If you keep your set-up as clean as you can, they will move to an easier target. That may be why some of your plot neighbours have issues with them and some don't.
There is a lot of conflicting advice out there. It sounds like you are having a good think through of the whole situation and not rushing in, so I'm sure you'll work out what its best for you