Anyway, you would get the best results from a base station if you want to listen from home. Portable units have a smaller range, but they can be brought into the airports to be used in conjunction with plane-spotting, so if you frequently travel to or near the airports, you should get a portable. As for which model you should get, that's a hard question, and mainly depends on your budget. Here's dave's suggestion from the FAQ.
In general, I suggest the following:
1) Bearcat/Uniden BC-780XLT, if you can find one and it fits within your budget. One of the best scanners ever made. Check on eBay since it is difficult to find new units for sale. The 780XLT has excellent sensitivity, covers the military airband, and has a computer control interface (via RS-232).
2) Bearcat/Uniden BC-350A or BC-350C. These are great scanners and represent great value. Lots of them on eBay. The BC-350C adds 800 MHz to the BC-350A (useful for listening to some public safety agencies).
3) Radio Shack has some great base scanners in the $80-$150 price range:
Pro-2052
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=20-432Pro-2018
http://www.radioshack.com/product.asp?catalog%5Fname=CTLG&product%5Fid=20-424