I think asteroid belts with a Gas Giant (or two) make the best Depots. That may be the type of system that is the Depot in the Spinward Marches, but I would have to look at the map again.
For me, Depots serve three main purposes. 1.) R&D, 2.) Training, and 3.) in-depth logistics.
R&D - Imperial Navy R&D would, in my opinion, be technologies or technological applications that are uneconomical for commercially sponsored R&D or is of such a military nature that commercial or educational R&D is not suitable (mainly for security reasons). Obviously, weapon systems top the list here, but survivability technologies may also be in this category.
Training - lots of things to practice gunnery, missilery, drop landings, 0-g maneuvers, vacc operations, etc. 'nuff said.
In-depth logistics - all the supplies to keep the sector's fleets stocked for multiple years at war time consumption rates.
A word about shipbuilding. I lean to the commercial shipyard model. It does make economic and security sense. Subcontracting can make sure no one contractor knows too much. Similarly, after a class of ship has been around there is not too much to keep secret. While depots can build and repair ships, during peace their focus would be R&D and prototype construction / special projects. Routine repair and new construction being handled by the commercial yards. During war depots would convert and crank out ships as well as repair damaged ones.