Hmm. When I pick ATG XIs/Squads, I work on the following assumptions:
1) The players would be plucked from the past in their absolute prime - for some players this is obvious; for others like Imran Khan or Sachin Tendulkar it is less so, as they evolved and changed so much as players over the course of their careers
2) The XI/Squad would train together for a few months before playing whatever hypothetical match/series/tournament they are being selected for. This helps builds team chemistry (so you don't necessarily need to pick Sutcliffe just because you pick Hobbs, for example) and helps to get everyone's fielding and fitness up to a certain minimal level, as well as getting the old-timers caught up on current day rules and regulations.
3) The latest rules/equipment/technology/nutrition/coaching/knowledge will be available to all the players. Apart from statistics ofcourse. So basically in preparation for whatever match they are going to play, they can view video footage of their opponents and study it, and vice versa.
This way you do have to consider a players' fitness, fielding and personality, but they aren't selection-breaking factors. Certain very old-era players do get disadvantaged (Grace, Barnes) because cricket was such a different game in their time, but talent will shine through in the end and so you can pick a squad without worrying about minor details.