I always have a spare tank, heater and filter- for raising fry, for healing fish, and especially quarantine.
The best reason to have a second tank is to protect the investment of your first tank. It can take six months to a year to build a stable community of fish, and it's horrible to watch it implode because you didn't bother to quarantine new fish.
What size? Depends on the fish you intend to keep. If any of your current fish will grow to be ~5 inches or more, then a 20g is the minimum. If you are thinking of buying a large breeding group to add to the big tank, their QT will probably need to be 40gal.
Because I have 8-10 tanks running at any given time, I can always move fish around to accommodate new/sick/bullied fish, but I still have a couple 10g tanks in a closet, and 40g in the attic. If I had to choose one spare tank, it'd probably be a standard 20g, simply because it's easy to find space to set it up on short notice and large enough for most fish for short term keeping.