Depends on the exact type of antenna you get, but in basic terms, yes, an antenna advertised as "450MHz" will usually cover quite a bit on either side.
Different designs of antennas will have different useable bandwidths. Usually higher gain antennas have narrower useable bandwidth, lower gain antennas have wider useable bandwidth.
What you need to look at is the antenna specs. Usually there will be something like "30MHz bandwidth at 2:1 SWR" That says that you can expect nothing over 2:1 swr (pretty acceptable) over a 30MHz wide area, so 445MHz to 465MHz.
The exact type of mobile antenna you need depends on your mounting, local terrain, where your repeater is, and most importantly, what your license allows.
You'd need to look at your license and see what the maximum power you can run in your mobiles. It'll either be listed as TPO (Transmitter Power Output), which is the measured transmitter power off the rear connector when terminated to a 50Ω load, or it'll be listed as ERP. ERP is the total of the transmitter power, minus cable loss, multiplied by antenna gain.
Running a high gain mobile antenna can potentially put you over the allowed ERP. While this may seem trivial, it can actually cause lots of issues for other users on the frequency. Your "footprint" might exceed your allowed area of operations and cause someone else licensed on the same frequency but in another area to have interference issues.
As for antenna designs:
- Go with an NMO mount. This is the de facto standard in the commercial/public safety two way radio industry. Using the standard NMO mount will let you use a wide range of antennas from many different manufacturers. The NMO mount is designed to be used in mobile environments.
- Go with a known good brand. Larsen, ComTelco, Laird, etc. Avoid the cheap Chinese/Taiwanese knock off antennas from Browning/Tram. You might save a few dollars, but you'll pay in the long run. Get a good antenna/mount now and it'll easily outlast your vehicle.
- Think carefully about your antenna choice. High gain antennas, besides the ERP issues, can work against you in mountainous terrain. I know you are in Hamilton, and that's pretty flat, but you said in your other post that the system is going somewhere else. High gain antennas work by focusing more power at the horizon. That can work well in the flat lands, but in high mountains, it can cause coverage issues.
Sometimes lower gain antennas will work better. Also, they are shorter and lower profile.
- Drill the hole and install the antenna correctly. It'll work a lot better and avoids the drawbacks of magnetic our temporarily mounted antennas.
Not sure where to order up there, but most amateur radio dealers will often carry a few of the commercial antenna brands. A simple 1/4 wave Larsen NMO mount antenna should run you less than $20.