If you mean a default *drive* (which I think you do), then no, you can't set it to use a specific one by default. However, you can use
Ultima's pSX Frontend to do essentially the same thing. It will always remember the last drive you selected, so after setting it up once, you can simply run it and select "Run pSX" right away every time you want to use pSX.
Setting a default drive is actually one of the more highly requested features for pSX that hasn't been implemented (yet).
If you literally meant *driver*, the configuration menu in pSX allows you to set whether to use ASPI or IoControl. For most all situations, this is better left to "Auto", but you can certainly change it if need be.