What'll happen? According to the schematic, nothing bad, since it says "minimum" load. From that, we can assume there's some safety margin in the output section of that amp.
Don't worry about underpowering a cab. Just listen for amp distortion and then back down if you hear too much. If it sounds clean or even just a little dirty, you're fine.
What cab to buy depends on a lot: the music you're playing, the room you're playing in, how loud the rest of the band is, whether your bottom string is E or B, and whether there's mains support for your bass. But if you were to ask me just to suggest a baseline to work from, I'd start with an Avatar neo 2x12 http://avatarspeakers.com/b212.htm
which would give you reasonable bass and reasonable midrange too, assuming a 4-string bass and a small club and the rest of the band behaving itself volume-wise. If you want to get a little more exotic (and serious), try Bill Fitzmaurice's Jack Bass http://billfitzmaurice.com/Jack.html
but build it with a 12. Depends on your woodworking skills. Or you can have one built. Whatever you choose, efficiency will be the name of the game in the context of only 70 watts. This is where the Fitzmaurice design would shine, the relative PITA factor WRT getting it built notwithstanding.