For me, like others have said, collapsed vs. curved varies from finger to finger from hand position to hand position. For instance to play D-E-F-F# on the D string with thumb-1-2-3, curved is natural and comfortable for me, and more importantly, pretty automatically in tune; however, to play D-E-F#-G with thumb-1-2-3, my first finger collapses at the last knuckle, otherwise it is significantly sharp. It depends so much on bass and hand size though, you really need to just do a lot of exploration on your own.
If pressing the string down is a problem, I think you should examine the way your arm as a whole is working. The weight of your arm should be resting on the fingerboard via your finger, as though it was dangling by your side and someone else picked it up and dropped it on the bass. Your arm is more than heavy enough to weigh the string down to the board. I hope this helps, but as always, face-to-face time with a teacher and self-exploration are probably fifty times more effective than anything we basstalkers can tell you.