The main challenge is the antenna. Especially for the lower HF bands. It's a challenge getting good efficiency. There are mechanical challenges as mobile antennas is out in the sun, wind and subject to flexing due high speeds.
10 metres (28 MHz) is the easiest band to get a mobile antenna for. A full sized quarter wavelength is 2.5 metres (or about 8 feet). 1.5 or 1.8m is much more compact yet still efficient. And you could cut down an old 27 MHz CB whip. Ten metres is great fun during the solar peak and in all years during the summer sporadic E season. It's also supports local communication. But otherwise you'd want capability for other bands.
40 metres (7 MHz) is a good all-round mobile band. Your antenna's efficiency will be severely compromised. But you'll still make contacts. 100 watts to a mobile antenna might give a similar signal as 5 watts to a full-sized antenna. And stations running 5 watts can make plenty of contacts on 40m. And 40m seems to be more sociable and less competitive than 20 metres.
Still, if DXing is your thing then 20 metres is a good choice. Especially if you can park at a favourable location near or over salt water. Then you might get out as well as a home station.
If you haven't built a mobile antenna before, make it for one band. It's easier. Then later you could make one with taps for other bands. Mobile antennas can comprise wire wrapped around a non-lossy material like fibreglass. That's continually loaded. You could have a wander lead with taps for various frequencies. And a sliding section at the top so you can make fine frequency adjustments (since good mobile whips have narrow bandwidths).
Or you could use metal rod saperated by a loading coil part way along. Base loading is mechanically better as the antenna's centre of gravity is low. But it's less electrically efficient than top loading with the coil at the top. Centre loading, with the coil in the middle, is a good compromise. Some builders add capacitance hats at the top for improved efficiency but these can attract attention.
Attention also needs to be paid to the base of mobile antennas. Not just mechanically but electrically as well. While a correctly built antenna at resonance may display a resistive impedance, it may be well below 50 ohm. Hence you can't simply plug it into the transceiver. You will likely need some form of transformer. This is discussed further in the better articles about mobile antennas.
If you'd like to try HF mobile with a homebrew antenna, here's some antenna ideas to enjoy:
* G3TSO mobile antenna experiences
* KM4IE $20 mobile antenna
* N1GY HF mobile antenna
* 7 to 30 MHz automatically tuned mobile antenna (from QEX)
PS: Want to learn about other antennas? You'll find many ideas and projects in the top-selling Hand-carried QRP antennas.