From Bob Fenner on
http://www.wetwebmedia.com/quaranti.htm
"A Quarantine System:
Is a smaller version (10-50 gallons) of a total marine set-up. It generally will have the following components:
1) A chemically inert tank of glass, fiberglass/wood, acrylic, +with a complete cover; possibly but not necessarily with a light fixture. Darkening the sides is a good idea.
2) Synthetic or "real" seawater. Some folks utilize their "spare" system to house, mix/age new water. I suggest you go the other direction and siphon "water changes" into the quarantine tank, and use a trash-can arrangement for preparing and storing new water. You want water quality to approximate your main system; what better way than to start with the water from there?
3) Some source of biological filtration. A sponge, cartridge-type outside power, or canister filter is better than undergravel, wet-dry or... You want to control the water chemistry in this system with a minimum of co-interaction with decor, gravel, mass populations of micro-organisms.
4) Test kits for at least pH, ammonia, nitrite and any therapeutic agent you might be employing (e.g. copper).
5) Chemically un-reactive cover.. PVC pipe et al. that will grant your livestock some sense of physical control, but won't absorb or otherwise change water chemistry.
6) Temperature control and monitoring. A heater and thermometer.
7) Treatment chemicals, nets, miscellaneous.
8) Oh yes; also a writing utensil and recording medium. Pen and paper to keep track of what you're doing and have observed."
I would run your filters when you start cycling your tank. The cycle process is to build up your bacteria load. Your filters house the bacteria, so, run them from the beginning.
Side note: By wet/dry, I suppose you mean trickle filter with bioballs? If this is going to be a full blown reef tank, I would not even start the cycle process with the bioballs, leave them out completely and let your live rock and skimmer do the filtration.