Our fearless commissioner, Beernoser, chose the 1935 New York Giants with his first pick. A good team, and flexible, too.
For hitters, he's got three terrific (if pricy) outfielders in Mel Ott, Hank Leiber, and Jojo Moore. Each costs in excess of $5.3M and logs more than 720 PAs, making them ill-suited for any kind of platoon at this cap. He's also got a great (if pricy) first baseman in Bill Terry (692 PAs for $6.7M). He's also got a great bargain third baseman in Travis Jackson for just $4M. His options up the middle are solid but uninspired. On the bench, he has cheap backups at most positions, but not SS or 3B. Hmm.
So we don't want to give him any help at C, 2B, or SS. Strength at 1B, 3B, or OF isn't that useful for him, but if I can also deny him any cheap bench options at SS or 3B, then that'll squeeze his flexibility.
The pitching side of the ledger is simpler: just don't give him any if you can avoid it. He's already got two strong, high-IP starters (Carl Hubbell and Hal Schumacher), one solid swingman (Al Smith), and a cheapo reliever with a terrific WHIP but a bad HR rate (Chagnon).
Looks like a job for the 1965 Washington Senators. You get one solid starting pitcher in Pete Richert, but beyond him, things get ugly in a hurry.
Not a single player on the entire roster costs less than $939K. Outside of Richert, the rest of the pitchers are borderline mop-up men with problematic HR rates. And on the hitting side, the only half-decent hitters play 3B or OF. And they've only got one SS and one 3B, so no backups to be had at either of these positions.
Good luck, Mr. Commissioner.