Well when you started this thread you rferenced the self-contained Xantrex unit and it seems to have a 51ah battery in it.
I have opened a lot of units and they all seem to use what I would call SLA batteries,sealed lead acid.
These days it seems that SLA and AGM are used interchangeably almost and I have decided that for my uses they are so I would use one labeled AGM or SLA.
All batteries can outgas if overcharged though even the so called sealed units which still do have venting built in just for this reason.
As long as you use a decent Smart Charger with a Multi-Stage Charge Program and it won't hit the battery too hard I think you will be just fine keeping these batteries inside and that is what I do in each of my trailers too.
I do enclose them somehow but mainly so they don't move at all or are able to get shorted by anything falling across the terminals unless it is me working on them.
I took these pics this morning to give yo an idea of the choices out there though these are not the only ones and in fact I don't have any 51ah models as are in that Xantrex box.
Every portable Jump Pack that I have opened had either a 7ah or 18ah battery inside and the 2 smaller ones that I show are what these look like.
The next bigger one here is a 35ah while the big boy is 80ah.
I use 2 of these 80ah in my Cargo Conversion and use a 20amp Xantrex Tru-Charge Charger to keep them charged.
I use a lot of the 18ah batteries for portable power and I use any decent 1 or 2 amp smart charger to run them.
If you go Solar you will need a Solar Charge Control to turn the Solar Panel output into a 12vdc battery charge level which most panels do not output natively though there are some that do,a controller is a good idea anyway to make sure the batteries are treated correctly for longest life and highest usability I think.
On the back end of the system if you do need to make 120vac from the 12vdc from the battery then you need to decide and calculate for yourself exactly what you think you will need and size an inverter accordingly.
Regardless unless you have a whole lot of battery do not expect a lot of useful 120vac power.