There's enough different "common problems" that you'd still need a wide variety of tools.

Starting tools would definitely be-
Allen wrenches
Combination wrenches
Spoke wrench.
A couple cone wrenches that fit YOUR bike. You can add other sizes as needed.
Assorted screw drivers.
I sometimes find a small (good quality) magnifying glass handy for inspecting small parts, but I don't have great eyes.

As suggested, look at the Park website to see what repairs/maintenance you plan on doing first and get those tools.