First off, you definitely want to have your MT fully charged to start with, and use your external first...in essence keeping it charged. If you run the internal down first it will demand more from the external to power it and charge at the same time, in other words it takes a lot less power to simply keep the internal on full charge than to constantly be charging. Plus depending on how old your MT is you may not get much time off just the internal...I know mine only lasts about 1/2hr nowadays.
I don't know much about the particular battery box you're talking about but it looks like it's just a 4xAA w/ usb out. Really, regardless of rechargeable or alkalines I would recommend having an extra set on you if possible. If you're just running for 2 hrs or so you should be fine with one set, but for 2 set shows that run 3+hrs I always preferred changing at set break just to be safe. If your just looking for alkaline battery suggestions Duracell is my first choice you should get 3-4hrs out of those. I'll let others chime in for AA rechargeable suggestions, there should be some pretty high capacity ones available, I'd look for ones at least 2600-2700 mAh or higher .
Long term you may want to look into the Macally IP-A481 battery, most including myself have had very good success with that one. It'll last a good 5-7hrs. Whatever you end up with your best bet is to set everything up and give it a test run, that will give you a good idea how long things will last for
you.
Here's a couple links:
rechargeable battery thread:
http://taperssection.com/index.php/topic,95539.0.htmlolder thread but other possible options:
http://taperssection.com/index.php/topic,51864.0.htmllink to macally battery
http://www.newegg.com/Product/Product.aspx?Item=N82E16855998033