Hey Fishman-I have the same size tank as you (20 G) and here's what I do to clean it:
I have the same type of syphon as orangecones, and a 5 gallon bucket. I get the suction started, then vacuum half of the gravel (I read somewhere to only do 1/2 the tank at a time, so you don't disturb too much of the bacteria on the gravel...not sure if it's true or not, but it makes sense to me). I generally take about 4 gallons out at a time, dump the bucket, then refill it, condition it, and put it back in the tank. Every few weeks or so I squeeze my filter media out in the old tank water, and every 3 months (approximately) I clean the filter impeller and the filter box (because algae grows there...or at least, some sort of green slime). I try to do a water change once a week...that usually doesn't happen, but it SHOULD! My tank is not heavily stocked (5 zebra danios and 4 guppies), which is probably why this has worked okay for me.
For water conditioner, I use the aqueon stuff. It has lasted me a LONG time now, over a year I think, and there is still lots left in the container. You really do not need too much water conditioner. My aunt and uncle have a small fish tank, and they just buy bottled water from the supermarket, and don't need to condition it b/c there isn't any chlorine. Of course, that probably isn't feasible with a 20 gallon tank, but it's another option.
I hope this helps! Definitely start gravel vacuuming, as it well help keep your tank healthier.