Ilford Delta 3200 is grainy. But the grain is beautiful. It's pointless to try to stop the grain from appearing. Film speed is gained at the expense of fine grain. That equation never goes away. You can use a fine grain developer, but frankly it looks better if you don't in my opinion. I routinely make 16x20" prints from 35mm Delta 3200 developed in Rodinal, a developer that most people avoid if they want fine grain. To my eyes, those prints look great, and I don't feel that the grain gets in the way. For portraits it may be a bit harsh in the grain department, but you take what you can get.
It is also a low contrast film. At an exposure index of EI 1,000 you'll have a nice grayscale with lots of shadow detail. This is the reason it pushes so well to EI 1,600, 3,200, even 6,400 without suffering in the shadow detail department terribly.
Without doing much testing, the best results will be had if you shoot it at 1,600 and develop it in Ilfotec DD-X according to Ilford's instructions as if the film was shot at EI 3,200. It sounds weird, but it usually works very well.
YOu can also experiment with push processing something like TMax 400 to, say EI 1,600. It works very well and will give you finer grain than Delta 3200, but probably a little bit less shadow detail at that EI.
My advice is to shoot a test roll before you photograph the event, so you can have an idea of what it looks like, and also to know if you need to make any adjustments.