Well, lots and lots of people tour on mountain bikes and do not have any problem with them. In fact, many prefer them as you can see by searching this (and other) forums. Particularly if your going RTW, many would say the 26' mountain bike wheel is more suitable, simply because tires and tubes for that size wheel are the easiest to find. Panniers or trailer? Up to you really, both work, it is just a matter of taste.
For touring, most will tell you to get a rigid rear on the bike. If your mostly on roads, get a rigid front also, you can always get shocks for when you get home and have a good off road bike also. With the kind of money you are willing to spend your choices are many. Bruce Gordon makes some excellent touring bikes, while many custom frame builders could do you well also. Waterford (and Gunnar) also make very suitable frames for what you have in mind.
Soma makes a very nice hardtail mountain bike frame (Soma Groove) that is relatively inexpensive (around $400 or so). I built one up for a tour I did 2 years ago (with panniers), and now use it for my commuter and have been very happy with it.
Whatever bike you get, make sure it fits you, and you get lots of saddle time before you leave. That way you can work out all the kinks before you take off.