If you want a small lead acid get an oddesey, they got a 16ah agm. According to the specs they can handle abuse better then the generic lead acids in jump packs, an oddesey cost about the same as the jump pack in your link, you would have to add your own connectors. I recently bought one of the oddeseys as a backup to my start battery, bought used for 80 dollars, its a nice heavy battery. The generic agms in jumppacks don't last long, I was always having to replace them. The oddesey can also be used as start battery in an emergency as long as you got the right terminals. The fullriver full throttle agms are also heavy duty lead acid batteries and usually cheaper then the oddesey, I have a 27ah fullriver that is almost 8 years old, I been using it as a start battery for the past 3 months since my interstate 12 volt wouldnt crank me over.
As far as charging any agm, even a small one 100 watts (5amps) will only trickle charge it, they can handle alot of charge current. I use to charge my 17ah jumppack with my 240 watt panel. No way to overcharge an agm with solar or even cigarette plug. Its next to useless to try to charge an agm with the cigarette plug, it charges too slow, you need thick gauge wires to charge at a decent rate. Even my 240 watt panel is only trickle charging my lead acid. AGM's like to be charge at high amps.
For your situation a small lithium power station would be a worthwhile investment. I have a 31ah lithium pack that I use as a backup to my house battery. I was able to run my 12 inch laptop about 5 days (3 hours a day) before I had to recharge it. It cost money but with lithium you won't have to guess if the battery is full or not, you can charge at your convenience unlike lead acid which needs to be charged right away.
Unless you run your car engine many hours, it will never fully charge a lead acid. It might charge to 70 or 80 percent, then the battery will require many hours to charge the remainder 30 percent. And if you don't fully charge it every day, it won't last long. Thats why having solar running all day is good, it fully charges your lead acid without wasting gas. Before I had solar I had to go to the library to charge my laptop for several hours, I just didnt drive long enough.
