There are no bikes that are good for both long-distance touring on roads and for single-track mountain biking. But if we can cross single-track off the list, and if we can cross fast club rides off the list, then almost any bike sold as a touring bike will do, and most of them are in your budget.
Both the Surly Long Haul Trucker and the Trek 520 fit your requirements, as well as many of the other bikes listed in the bicycle buyer's guide right here on this site.http://www.adventurecycling.org/resources/201004_TouringBikeBuyersGuide_Schubert.pdf
Here's my recommendation. Print out the guide. Go visit all of the local bike shops in your area, including REI if you have one. Ask them which of the bikes on the list they have on the floor (probably none). Then ask them which of them they can order for you, without obligation. Ride two or three up and down the steepest hill around. Buy the one that feels the best to ride. If two both feel good, but the one you like the looks of best.
Don't fall into analysis paralysis. There are many bikes that will do just fine. Don't worry about getting the "best"--there is no best. Just get one that meets your requirements and fits you like a glove.
If you have no bike shops near you, or none of them are willing to order a bike for you without obligation, then determine your size using online sizing guides and order either the Surly LHT or the Trek 520, whichever one you like the looks of best.