Do you want to run the drain down the joist bay to the opposite end and keep going horizontal with the drain past that wall above?
If so, per the Wisconsin plumbing code, you can use a 1-1/2" trap, run the trap arm at exactly 1/4" per foot, and have the vent connection up to 6' away when you use an upright horizontal combo for the vent takeoff. Or if you need more than 6', you could can use a 2" trap (upsize from 1-1/2" on the inlet side of the trap) and go up to 8'. The 1/4" per foot is critical here, as that is the minimum pitch, but the total fall is limited to one pipe diameter (hence 6' for 1-1/2" and 8' for 2").
If your drain turns downward where the vent comes off, then the Wisconsin plumbing code has lower limits on how long the trap arm can be, see Table Table 382.31−1 "Maximum Developed Length Between Vent and Trap."
Cheers, Wayne