[ while searching for an antenna. I noticed there were quarter wave, no ground, wide band, and high gain. What is the difference between these?
Physically shorter antenna. Requires a ground plane under the antenna to work correctly. Lower height can be a benefit on taller vehicles. 1/4 waves also have a nice round radiation pattern, which can work well in the mountains or hilly terrain where the other station you are trying to connect with could be well above or well below you. Quite broad banded and a good choice if you need to work on frequencies spread across the band. I use these almost exclusively, and when I put them on an analyzer, they'll give 2.0:1 SWR or less across the band, from 144MHz (amateur radio band) to well up above 160MHz.
0dB of gain.
Least expensive antennas (usually). Can be purchased for $10 or so, and work quite well.
Doesn't require a ground plane under the antenna, but works better with one. Good choice when you need to mount the antenna on a truck mirror or on a vehicle that has a fiberglass roof (RV, etc). When installed without a ground plane, they have the same amount of gain as a 1/4 wave. When you install them with a ground plane, they provide about 2.4dB of gain compared to the 1/4 wave. These antennas will be twice as long as the 1/4 wave.
Partially a sales gimmick. A standard 1/4 wave is very wide band. There are certain tricks they can use to increase useable bandwidth, like making the antenna whip thicker. This is a good solution (along with the 1/4 wave) if the frequencies you are going to be using are spread over a wide area of the spectrum. Usually this is where you have channels down around 150MHz but also need to use the federal portions of the band up around 170MHz. Usually it's not required in most cases.
Physically longer antenna. Good choice when you are out on the plains and the stations you need to communicate with could be way out on the horizon. They usually have 3dB or more of gain. This effectively doubles the transmit power, but it does this by focusing the radiated power out towards the horizon. In some cases, like in the mountains, this can be a drawback as the performance will drop off if the other station is much higher angle above or below you. Longer antenna can be an issue on tall vehicles, hitting branches, parking garages, etc. Also, they tend to have a much narrower useable bandwidth. Fine if all your frequencies are within a few MHz, like on the amateur radio bands, but can be problematic if the frequencies you use are spread out across the band. Cost more....
I'll add a few things:
1. Higher gain often is an attractive trait in an antenna when you just look at the gain numbers. Since the higher gain focuses more power at the horizon, it makes it look like you are running more transmit power than you actually are. A lot of times people will see this as "free" power and think they scored the deal of the century. In reality higher gain antennas can work agains you in some situations.
2. No manufacturer has any sort of magic pixy dust they add to antennas that will make them break the laws of physics. Antennas are not magic, they work a certain way. Some manufacturers will tweak numbers, make claims using "alternate facts", etc. to try and make their antenna look better than another. Doesn't work that way.
3. Avoid the cheap Chinese brands. Browning, Tram and the off brand stuff might save you a few bucks, but you'll end up paying more in the long run. Don't waste a perfectly good radio like the TK-790 with a crappy antenna.
4. Go with the NMO mounts. They are the de-facto standard in the industry. Once you have that installed, you will have your choice of many different brands and styles.
5. Often the $10 quarter wave antennas work just fine. Don't get blinded by the gain numbers.
6. Do it right the first time. A properly installed quality antenna will easily outlast your vehicle if it's properly maintained. Cutting corners will lead to disappointment, headaches, etc.