So, I recently did a whole design study on the 1S/2S thing.
1S Packs+ HEAPS of charger ICs available
++ Quite easy to protect, no balancing required
+ If you can run your electronics down to 2.7V, works well with 3V3 LDO
- If you really need 3.3V and high current (to run that motor) you'll only be able to use half the cell before hitting your low voltage limit. Or you'll need a buck-boost converter.
-- You'll need a boost converter for your motor supply
+ Your boost converter could provide constant voltage for the motor driver
3S Packs- Fewer charger ICs available
- Make sure it's got a proper pack protector. You may need balancing.
+ Voltage always >3.3V, so you can use a buck regulator
- Using a 3.3V LDO quite inefficient
+ Can run motor straight of pack, no need for boost converter
- Supply voltage to motor will vary with battery charge level (and motor current and temperature)
Can I ask some more questions about the application? There are a lot of factors in battery selection...
- What temperature range are you expecting? Rechargeable batteries don't much like going below 0C or above 40C.
- When you say 'as long as possible,' do you mean 'as many hours as possible on one charge' or 'as many years as possible before the batteries crap out'? The two goals are a bit contradictory.
- Are you making a tool for you or some kind of product?
- Do you need to charge the battery inside the device?
- What is the acceptable voltage range for your motor & driver? If you don't need maximum speed, it may be possible to run at reduced voltages.
- Please do give us the info on actuator consumption. Will the actuator spend most of its time idle or moving stuff or holding stuff?
- What consumption do you expect to happen at 3.3V? If the actuator is often idle, this 'standing' load can turn into a big fraction of the total battery consumption. I would consider using a buck converter for the 3.3V supply, especially if using a 3S pack.
- Keep in mind that improvements in efficiency can turn directly into increased run time, and lower temperatures - which will improve battery life.
You'll also need to have a look at acceptable voltage ranges:
- LiPo / LiIion typically work over the 3.0 - 4.2V range (3.7V average). So a 3S pack would be 9.0 - 12.6V, roughly. This is a bit below a 12V lead acid.
Typical lifetime is in the hundreds of cycles. - LiFePO4 batteries (sometimes called LiFe) typically work over the 2.7 - 3.6 range (3.2V average). So a 4S pack would be 10.8 - 14.4V, which actually lines up quite well with a 12V lead acid system.
LiFePO4 batteries store about half the energy by volume (vs LiIon), but last for > 1000 cycles.
Okay, then I would choose a 3S1P, but most of the packs that are available, are not that high capacity. On the other hand, there are 1S batteries with quite high capacity (but low current delivery). Is the solution building a custom 3S1P?
Building a custom pack is not very hard these days (don't forget some kind of pack protector). Ordering custom packs is very possible, but you can run into trouble shipping lithium batteries. Have you looked at RC Helicopter / Drone battery packs? You may be able to buy them locally.
If you're making a commercial product, try very hard to keep below 10 Watt hours per cell and 20 Watt hours total, or shipping your product becomes very hard.