Li Ion typically can do 300-500 cycles so that includes 600-1000 half cycles. Deep cycles doesn't age more than you are just cycles.
So larger batteries last longer as for any given energy it is fewer cycles, but bigger batteries weigh more and cost more. So don't worry about, you just need enough energy with you.
Ah is a nonsense metric of energy, you need Wh, which can be made from Ah x Volts. You mentioned Ah but not V so it's a nonsense ask.
If you want to user an inverter it will lose 10% of the energy.
So take the AxVxh of your device to get What, then 0.9 for each step. So if you wanted to use Anker USB product like. 20000mahx3.7V (typical voltage of the cells to get 74Wh. Then if could find a 5V to 19.2V it then is 3.85Ah but then remove the two steps out of the battery and the inverter so 3.12Ah