INTs, if anything, involve more luck than fumbles. Not a lot more, but they do involve a defender being in the right place at the right time. The bad decision or throw is a result of the defensive pressure on the QB but that alone is not a turnover. The second component of an INT, the actual catch by a defender, involves enough luck that a defender happens to be in the exact location that the bad throw/decision sends the ball off to... in short, QB pressure causes incompletions, scheme and a little luck added on top causes INTs.
When I say third priority, those priorities are very, very close. Most fumbles happen in traffic, which gives a tackler more freedom to try and create a turnover because there are other defenders in the immediate area. Now, if you move that play into the open field, of course the tackle itself becomes top priority and creating a turnover is secondary. The priorities also shift themselves out a bit depending on the defensive position. A CB, for instance, is almost always "just make the tackle", but an LB will definitely be looking to create a turnover just as much as tackling an RB coming over guard. The LB also has a less overt task of hurting the RB each and every time they come into their coverage zone. The goal there is to make them go someplace else next time, taking away an entire section of the field from the offense.
EDIT: Forgot, I was going to address the "no wonder they miss so many tackles" comment. That's a valid observation about NFL defensive backs. They have an increasing tendency nowadays to try for the big "SportsCenter" hit rather than making a proper tackle. Some will whiff entirely in the attempt or at least end up so out of position they can only make a crappy arm tackle attempt. You don't see that as much with Linebackers but the highlight reel syndrome is very real among defensive backs in the NFL. If you go to a high school game, or 99% of college games, you won't see that as they don't have highlight reels.