I would deffinately seal all the joints inside and paint it. The Killz is just a primer it's not going to offer much protect for the wood for long. I would use something with a high gloss finish for durability. If the OSB gets wet it's going to swell and over time will begin to fall apart. I didn't catch whether or not you were going to run a sump but if you are then you have to figure on at least a few gallons of evaporation going on under there every week. Over time it will wreak havoc on the stand if you don't.
I've done minor trim work by hand before, it's not that bad if you don't have to do a ton of it.