Hi,
Since you only have a few fish etc, starve them the day before the move, bag them up or put them in a tupperware tub, if you bag them put them in a polystyrene cooler to keep the temperature up.
Drain the tank, bag the filter to keep the media wet, since its quite a small tank you should be ok to lift it with the substrate in if not bag as much as you can, bag any live plants.
Get to the new house place tank where you want it, fill it with dechlorinated water and turn heater on to get it to correct temp, add everything you removed minus the fish. Add the fish once the temp is ok. The fish will be fine if they have to stay bagged all day but bacteria will start dying in the filter after a couple of hours. If you can't set the tank up the same day put the fish in a tub or bucket with the filter and heater running until the tank is set up.
Take the tank in your own car unless the removal company are insured for fish tanks. Pack it last then it can be unpacked first.
Hope this helps
Emma