Edging can go either way, depending on what you are working on. Models that are simple in design and expose all their raw edges (like a wall) are easy to edge after the fact, but some more complicated models are a lot easier to deal with if you edge them as you go, because once assembled, some of the edges are hard to reach.
As for cardboard...I don’t recommend using it in place of foamcore, as it isn’t generally as durable. However, thin cardboard can make for tougher walls if you want to use it and modify the wall design somewhat.
One alternative to foamcore I’ve used for basing is vinyl tiles. They’re pre-glued, and quite durable, and if you get their worst-looking cheap version, they’re cheap. Problem is, they’re also 12” square, so you can only get one 7” by 7” square out of a tile. If you don’t mind “tweaking” things a bit to go to 6” or 12” tiles, though, they work really well and are very cost-effective.