It seems only recently that some browser makers are taking fingerprinting seriously. Running multiple browsers seems like a good solution until you realise that most browsers still reveal far too much distinctive detail about the software and device they are running on. Unless you run these browsers in isolation from one another (e.g., in specially configured VM instances), it is more likely that each browser will only create another distinctive fingerprint to be correlated with your other browser "identities". (And it probably won't take long for that to happen.)
If you're particularly concerned with browser fingerprinting Tor Browser is probably your best choice. Although it still stumbles a little in making all TB users look exactly the same (a fundamental intent in its design), TB is still far more aggressive in this aspect than other mainstream browsers. Incidentally, with version 9.0 Tor Browser now enables "letterboxing" functionality intended to help mitigate the browser viewport fingerprinting you touched on.
Because it is always troublesome to do online banking and shopping with either Tor Browser or lynx, I use yet another browser almost exclusively for these purposes. I find it very annoying (and a waste of my time) to have to use three browsers.
Certainly, but only a degree — your screen resolution is just one of many attributes the machine learning algorithms use to separate you from other users.