From the look of the terrain around you (low rolling hills, correct?) you might be best served by an antenna with a bit of gain. They tend to have a fairly flattened out pattern, when compared to the quarter wave, and would be expected to work a little better where you had a good view of the horizon all around. If you were in deeper valleys, with taller hills around, the quarter wave -should- work better (but not necessarily). One thing you can do is take a look at what the local public safety agencies are using. If they are on VHF, a quarter wave will be 16 to 18 inches tall. If on UHF, the quarter wave will be 6 or so inches tall. If they are using 5/8 wave, a VHF will be around 45 to 47 inches, and a UHF will be about 14 inches.
Real world experience will tell you for sure, one way or the other.
Quarter wave antennas are usually cheaper, so it would be a good place to start. If it worked satisfactorily, then you'd be good to go.
You can find the 1/4 wave NMO style antennas pretty cheap, as you discovered. You might even want to look at the specific frequencies you want to listen to and cut the antenna for that. A new antenna should come with a cutting chart. For receive, it likely won't make noticeable difference, but it wouldn't hurt. If most of your listening will be in the public safety bands, you could cut your quarter wave for around 16 inches long. A short quarter wave like that, on top of a car, truck or van, will be lower profile, and less likely to hit trees, parking garages, etc, than a 5/8 wave.
You just need to decide on where and how you want to mount it. NMO mounts are about as standard as you can get. If you start there you will have a wide choice of antennas to choose from.
Permanent mount, magnetic mount, trunk lip mount, fender bracket, etc, you'll have to do what you think you can do. A permanent mount is really nice, looks professional, and if done right, will give you a lot of years of trouble free service. I've installed them on vehicles and they are still working fine after 10 years. Installation is pretty easy, but not for everyone.