1st of all, to shoot deer one would be better off with interchangable chokes - to reduce choke for shooting slugs or ball for deer, and shot for birds and larger shot for fox.

What makes of guns are available to you?

Do you handload or must you use factory ammo?

A pump-gun with interchangable chokes would better serve, I'd thing and cost less.

If money is no impediment to purchasing something expensive, then I'd pick something in a high priced Italian Double and have them make me a couple rifled chokes for it.

The effective range would be the range at which I could hit with ammunition that was effective. Usually 60yards max on grouse-type birds, 40yards with large shot, like BB for fox and possibly 100yards on deer with slugs IF the gun shot the available ammunition accurately enough.