Can you get a Good- or Best-Craftsmanship vehicle? And if so, what kind of benefits would the better Craftsmanship provide the vehicle?

I'd say you could get a good or best craftsmanship anything, but there aren't any formal rules for what benefits that those things would confer.

I'd start with giving the "reliable" special rule (+20 tech use to repair, if I recall) to better quality vehicles. Upping armor protection without dropping speed because of the higher quality alloys used in the construction of the vehicle might also work.

Giving some bonuses to drive or pilot tests because of the vehicle's superior handling would also be a good start. Maybe +5 for good and +10 for best.

Or you could go the other way - its not better but its older and/or has a history attached to it. Owning (and showing off) the vehicle gives you positive modifiers to one imperial faction (eg. Ecclesiachy - it was once ridden by a saint; Imperial Guard - played a key role in a famous battle; Imperial Navy - launched the bomb that crippled a xenos cruiser; Inquisition - personally gifted by a power Inquisitor Lord in return for a favor; Adeptus Mechanicus - vehicle has a trivial archeotech component, such as an extremely advanced holo display; Space Marines - your ancestor saved a chapter master with this vehicle; etc... )

You could also reduce the number of crew required in some cases. A best-quality Leman Russ, for example, might be from a Forge World's own Tech Guard. It might have autoloaders, remote control sponsons, and perhaps a strengthened machine spirit.