In everyone's estimation, when considering a player for serious training, what are the bare minimum requirements?
It depends on what you want from your players. Personally I tend to look for decent secondary skills so that I get more rounded players when I train all the primaries up. Some people look for decent primary skills so that they can train up a single skill monster with little secondary attributes. And of course, what 1 person considers a vital skill could mean nothing to another player. It's best to look in the forums and get a feel for what you think you want from a player in a certain position.
What about potential? how big a factor is that?
Again, it depends. Potential is only a limiting factor - all similar players will train a skill at the same rate, but those with a lower potential will see a reduction in training speed sooner than those with higher potential. If you're looking to train for a season or 2, potential isn't really that much of an issue. If you're looking to train up some NT contenders over the course of 3/4 seasons, then perhaps look for trainees with high potential.
What is the highest skill level that a draft pick could come with in any given skill?
I don't know for sure, but I'm just guessing at
strong? Perhaps someone else could confirm/deny this.
Also, does wage change every week, or does it get recalculated at a different time?
Wage is recalculated at the start of every season, so what you see at the moment is what you'll pay for the rest of this season. Except for staff. They get a pay rise every week, the cheeky sods!
Hope that helps you out a bit.