Should I sue my partner directly, or sue the partnership itself?

This genuinely depends on precisely who or what was actually harmed by the conduct you're complaining about. A direct claim is the appropriate vehicle when the harm was done specifically to you personally, as an individual partner, separate and apart from harm to the business itself. A derivative claim, by contrast, is brought technically on behalf of the partnership entity for harm done to the partnership as a whole, and this type of claim carries additional procedural requirements, including typically a formal demand made on the partnership's managers before you're permitted to proceed.

Getting this fundamental distinction wrong, filing a direct claim for what was actually harm to the partnership entity, or vice versa, is genuinely one of the most common reasons these complaints get dismissed or significantly weakened early in the litigation process, before the underlying merits of the dispute are ever properly addressed.