If you're only going to repeak your packs and not be charging you can easily get away with a 7.5ah battery, that's a conventional size which is usually called a 7-12 (7ah, 12v) you can also use a 12ah or a 18ah, anything larger and they become kind of a hassle to pack around.
The 7ah battery is about 6x3.5x3.5", a 18 is about 7x7x3.5 and around 14lbs. So it's manageable to pack around and will still fit in your field box.
"deep discharge" your probably refering to Deep Cycle - these are lead acid batteries that are designed to be able to handle more discharges (cycles) than your typical auto battery. They are designed just for putting out low current for a long period of time. Each time you cycle a lead acid battery it wears on the internal plates, essentially deep cycle batteries have thicker plates that resist wearing out longer. But when talking about the sealed gel batteries, these are considered AGM batteries and can be used just like a deep cycle as the way they are constructed makes them handle multiple cycles fine. AGM's are most used in battery backup systems and wheel chairs that see frequent cycling.
Depite the price, I would not purchase any of the ones you'll find online for mega-cheap deals. The brand X batteries are low quality, spend a little more and go to like interstatebatteries.com and buy one of theirs.
Here are the batteries I'm talking about ..
For the price I'd buy the 12AH one myself, as you can use it to fully charge your discharged packs multiple times without issue. In theory you should be able to fully charge a 3300mah pack about 4 times off a 12AH cell, even with charger loss and heat.
On the other hand, if you want to pack around a large battery you can purchase a deep cycle wet cell that is anywhere from 90ah-115ah for around $60 at the major chain stores like Fred Meyer, GJ Joes, etc. But it is much heavier and not clean at all.
Also about those jump boxes, it depends on the box but they typically have two 6v 10AH cells but I've seen them with only two 4.5AH cells.