Cheap car battery - yes, it'll get you through one night!
Actually if you don't pull it too low before recharge, you may get some life from it - but don't expect long life. I used one for some months. Last weekend I put it into my car where it will have a happier life. I now have an AGM battery for my astro needs (which are just heaters and Argo Navis).
Traditional vented/flooded lead-acid car batteries are designed to push out cold cranking amps (CCA) to get your car started from cold, then to be recharged immediately and held at charge until the next engine start. They are not designed for lengthy flows of low currents. For our applications we need what are called deep-cycle batteries.
Here are some useful articles:-
http://www.batterystuff.com/tutorial_battery.html
http://en.wikipedia.org/wiki/VRLA_battery
http://www.vonwentzel.net/Battery/01.Type/index.html
After the battery, a good intelligent charger is very important. The el-cheapo charger (like I first bought) may well do damage over time.
I use this one from Jaycar:-
http://jaycar.com.au/productView.asp?ID=MB3606