If you have a max game requirement of 162, how do you fill it with only 3 players besides your starters?

You need at least one extra catcher, a middle infielder, a fourth outfielder, an extra first baseman....

That's four right there.

I'd want a major league sized roster of hitters. As long as you stick to the 162 game max, the extra guys add more strategy elements 'cuz you're not simply playing the same eight guys every day. Plus, larger rosters encourage trading, as you've pointed out.