I got to give you credit for at least having a reason for wanting UV. Far to many people want one for no special reason.... I mostly want UV for parasite issues. In my short time in the hobby, LFS stock has subjected me to cotton mouth, then internal parasites and I now have ich. This is stressing me more than the fish!
The problem is that UV can only kill something that actually passes through the unit. With most of the diseases you mention, enough of the pathogen will remain in the tank to infect the fish. You often see UV used in LFSs because it can stop disease from spreading to additional tanks. It does comparatively little for what is in a single tank.
Also, with UV, generally the more complex the life, the more UV you need to kill it. It takes a lot more to kill ick than is does algae spores.
If you are going to invest in a UV unit, I'd suggest, oversize it. Get one rated for a tank about double the one you have.
All that being said, I think you'd be better off finding another LFS, one that takes better care of their livestock. I would also consider investing in a quarantine tank, and quarantine all new fish for a few weeks before you introduce them to your main tank. A quarantine tank can be minimal, just the tank, sponge filter, heater and a few rocks or PVC pipe fittings for hiding places.