That's too many darn cats. Like the earlier poster said, it's pretty difficult to try to craft any kind of "strategy" when you have that many different factors.
In terms of positional drafting, my strategy would be roughly along the lines of:
Draft a power-hitting 1B early. After the first 6 or 7 it gets weak.
Also go with a strong bat OF early, too, as there will be a premium since you need at least four for every roster.
After that, fill in your infield, probably looking at 3B and SS first, then 2B. Don't go with an SP until at least round seven or eight, then take the best one there. Fill in the rest of your offense, then grab SP and RP depending on quality available, with an emphasis on SP first.
That's pretty basic, and I'm probably not thinking enough about this, so if someone else wants to dispute what I'm saying here, please feel free to offer a second opinion.