Lead acid batteries are ill suited to this application, they are designed for short bursts of high current (ie starting an engine) and then a nice slow recharge. They don't like being drained and recharged, you need deep cycle batteries for this (on a large scale, like solar). Lipos are also good for this, any decent size Lipo can put out 5 amps for the entirety of it's capacity.
To select a proper Lipo you need to know what you want out of it. "A decent amount of battery packs" is terribly vague
That could mean 35 1s 150mAh packs or 35 10000mAh 6S packs. It's all about energy. Volts x amp hours is watt hours. Calculate what you need (ie a 2200 mAh 3s would be 2.2 x 11.1V = 24.42Wh) Then find out the max voltage your charger can accept as input to determine the cell count you want. Say your charger can accept 24V - the biggest you could go with is 5S - 21V fully charged. 6S is 25.2, which would kill your charger eventually. Say you want to recharge 6 of the 2200 3S packs above, that's 146.52 Wh. To get the capacity you need at 5S, divide 146.52 by the 5S voltage of 21 = 6.977 amp hours, or 6977mAh. Then it's just a matter of shopping for the battery you need. Less expensive, low C rated lipos are perfect for this.
Math. It's always math