This article covers a lot of parameters in detail:
http://www.reefkeeping.com/issues/2004-05/rhf/index.htm
I think it's worth reading.
For the basics, I'd check temperature and salinity regularly. Hopefully, your refractometer is calibrated with a saltwater standard. Alkalinity helps with pH, so I'd check that, too. Corals require calcium, and can consume a lot of it, so I'd keep a test kit on hand if I had corals.
In emergencies, an ammonia kit and something like Prime or Amquel are good to have on hand. Phosphate, nitrite, and nitrate kits can be useful for diagnosing coral problems. pH can be worth checking in rare cases, and a probe or meter is more accurate than a test kit.
A controller with probes would be a reasonable way to measure salinity, temperature, and pH, but they aren't a necessity. I wouldn't bother with ORP, personally:
http://reefkeeping.com/issues/2003-1...ture/index.htm