I'm guessing the application you intend is to use UV curing resins by mounting a powerful UV source behind a diffuser lens and LCD screen as a light blocker. The LCD is kept just above the surface of the resin as the tank is filled and the LCD rather than the UV LEDs provides the image resolution. If this is the case, the LEDs can all be the same brightness, which is an advantage because you can use different voltages, 54V for all 15 LEDs in series, 18V for 3 strings of 5 LEDs, 10.8v for 5 strings of 3.
It's a benchtop device so you can get away with things being a bit bulkier, which will make things easier for you.
Cooling the LEDs is important, so you may want to look around the usual DIY sources for some massive aluminum heatsink or a bunch of smaller ones depending on how far apart the LEDs are. The MCPCB stars that most power LEDs come mounted to are actually usually adequate for low power, especially with current control, but if you're going to have 15W together in an enclosed space beside an LCD you don't want to heat up, it wouldn't hurt at all to keep it cooler. This will also help avoid a long heat up time while you wait for the LEDs to reach thermal equilibrium and for their brightness to steady. LED efficiency also improves if you keep them cooler.
As for a driver, because it's a desktop unit you can get yourself a constant current LED driver of appropriate voltage range for the series/parallel arrangement you decide to use. They're usually about 4-5 inches by 2 inches by 1 inch or smaller depending on power rating. 120 or 240V goes in, constant current comes out to drive the LEDs. If you choose one that's dimmable you'll be able to adjust brightness if you want.
Here's a link to the section on DigiKey. You can find this sort of thing at numerous websites and sometimes even hardware stores, so you can use this to get an idea what you're looking for. Just fill out columns with things you do know, one at a time, and use "apply filters" in between until you narrow it down. Constant current is usually used with LEDs to eliminate thermal runaway without using series resistors.