Hey Jack, welcome to LiveATC! I'm not a huge expert on scanners so I'm sure somebody else will give you the details but here are my 2 cents...
Make sure you find one that can do airband... 108-136MHz is the range for airband (though I think some say 118-136?). If you want to disconnect and take it to the airport to watch sometimes, a handheld may work better than a base station. Most are pretty standard though, with a BNC connector, memory+scan, squelch, etc. Don't forget - an external power source is needed if you're setting up a feed (unless you like changing batteries very often).
Beyond the scanner, antennas are also important. Unless the airport is your neighbour, a decent antenna is also good to pickup various controller and pilot.