Matt,
I would say, in general, a 13 foot match-style rod is sufficient. I prefer a 14 footer (Daiwa Aqualite) myself as I find it gives better control. However I also use an 11 foot (Greys) on my local tiny river due to the overhanging trees, etc.
Always coupled with a centrepin (loaded with 4lb mono) ... most of the rivers I fish are 2 to 4 rod lengths wide and a 'pin (I find) gives much better control over the float.
This sort of tackle will handle chub (unless it's really snaggy when you need to bully them) but if you get after barbel you need to step up to an Avon-type rod as you won't really be in control

Although you can exert a fair amount of pressure with a light float rod you can't bully the fish in ... you coax a big fish in.
The problem with a fly rod (imo) is the handle and the rings. You need to have a bit of handle (about a foot or more) to balance the rod and for bracing against your forearm when playing the fish. I would imagine the action of a 10' #3 rod would be fun to use for trotting ... but where's the fun in that? We all need to buy new toys to play with