Speaking of Mike Brown and his planets, if the proposed Planet IX is confirmed, then it's likely to be about 700 AU away. That's a 200 year journey at "Voyager" speed (~3.5 AU/year), so we'll need to go significantly faster.
For historical precedent there's the Thousand AU mission design from the late 1980s, which used a SNAP powered ion drive to push a probe to ~20 AU/year. Waiting 50 years for major data return seems excessive, so I'd think a 20 year max travel time, and preferably a 10 year travel time, should be in the minimum specifications.
The main propulsion options IMO are an extreme Oberth Maneuver, with a very high thrust system at perihelion; a high performance Solar-Sail; an E-Sail, and - a bit more speculative - a laser-push by the proposed Starshot Array.
Anything missing?