If you want to start cheap, before learning more about what you really want, you can get a Beofeng UV-5R for $20-$25, unlock it (to get a bunch more frequencies), and use it's "Scan" feature.

It's not going to have the features of a scanner, but it will let you listen to analog transmissions for a lot of bands, and can be used to transmit, if needed for an emergency, etc.

I use mine on unlicensed frequencies for work.