If your primary focus is your fathers side, I would test him first. You only inherit 50% of his DNA so you could miss many of the matches he would have. (I have both myself and my mother tested and about half of her matches I don't have on my list).

Later, if you want more info on your mothers side, you can have yourself tested. You would then compare your matches to your fathers and the ones that are not on his match list would be from your mothers side.

Even if your interested in both sides, I would do your father first. It takes a lot of time and effort to figure out where a "match" is related (sometimes its impossible) and you could work on his side of the family while waiting to decide if you want to be tested too.