Delta 3200 is an ISO 1000 film.

With its inherently lower contrast it is designed to respond well to being exposed at an exposure index ("EI") of up to 3200, and then push processed to bring the contrast up.

Talk to your lab about what their experience is with it, and how they approach their pricing for their services.

It may be that their "standard" processing routine for Delta 3200 is the "push" that best suits use of it with an EI of 1600 or 3200.

I know many like to use the film with an EI of 1600, and then develop it for the time recommended for an EI of 3200.

And at the risk of being pedantic, "push" and "pull" really doesn't refer to exposure, but rather development only.

I prefer to refer to "increasing" or "decreasing" exposure instead.

Hope this helps.

EDIT: in case you haven't reviewed it, here is Ilford's "Fact Sheet" for the film: