As always, it's a bit of a compromise. Breaking strain, abrasion resistance, diameter & stretch (or preferably lack of it!) are all things I look for, as well as resilience after pulling from a few snags! I've used some lines that are good in some respects but proved useless in others; I particularly remember trying that Ultima Powersteel stuff a few years back. First impressions were very good - nice & smooth, cast well etc etc, but after a couple of uses & pulling from a couple of snags it seemed to lose all strength & started snapping like bait elastic!........so in the bin it went.
I tend to buy line by diameter; 0.35 for clean ground, 0.40 for mixed & 0.50 upwards for rough stuff. For me, one line has proved consistently good in all three and that has been the red Suffix Tritanium - sadly this is no longer available so when my current hoard of the stuff runs out I'll be looking for something to replace it, hence my recent trial of the new Berkley stuff. I used to use a lot of the Trilene Big Game - another very good line but just a little thick & wiry for my liking; so far the XTS is looking like a good contender as a replacement. The only downside (for me) is that it doesn't light up at night like the Tritanium does when you shine your lamp on it; I really like that hi-viz aspect of the Suffix stuff.
Personally I wouldn't go below 0.50mm line for real rough ground either - I don't care what the stated breaking strain is but my feeling is that 0.50 is as thin as I'd want to go to cope with a few scrapes from rocks etc. For short range plopping into real heavy stuff I'll step up to 0.60 or heavier, without a leader - the disadvantage here is that if you do chuck a bit further the amount of line left on a "30" size reel will be almost nothing, so you lose a lot of speed on retrieving your gear. I've found my 30 size reels will hold about 240 yards of the 0.50 stuff, so that really whacking out a clipped down bait will still leave me half a reel-full or so, giving me a pretty good rate of retrieve to get gear, or a fish, up & on the move pretty quickly.
I guess in order of priority I look at:
Diameter.
Resilience (a combination of abrasion resistance & strength & how much use I'll get from the stuff before having to re-spool).
Low stretch.
Stated breaking strain.
Gary