Deep cycle are better for charging and discharging but they are expensive and large. I have never seen any small true deep cycle batteries in any shops. An ideal one would be the lead acid batteries used in coal mines for the miners cap lamps.
Many disagree, but I would say avoid gel batteries as they dry out too easily.
I find small cheap wet type (non sealed) motorcycle batteries great but remember these are not designed to be drained right down to 10.2v like a deep cycle battery. Just drain them to 11.2 and immediately recharge and they last for many years.
Car batteries are too big for a single fan unless you have one of the really big ones, again don't discharge below 11.2 because these are starter batteries.
There are many factors effecting charging time the biggest being your supply. If your battery is 100Ah and your supply is 1A then its going to take 100 hours or more to charge the battery. Find out how much current your fans draw and multiply that by 20 and that is the ideal Ah rating of your battery but in my experience anything between 10 and 20 seems to be fine.
C20 is the Ideal charge and discharge rate of lead acid batteries, that is you charge or discharge them over a period of 20 hours. They are more efficient and last much longer if used at this rate.
The Amp hour rating of a battery is the theoretical amps that the battery could deliver for 1 hour continuously before becoming discharged. In truth the battery will be flat in probably half to 2/3rds of that time at that discharge rate. With deep cycle batteries it is different they will give that current but you will notice that a 20Ah deep cycle battery is as big and more expensive than a 100Ah car battery. You could consider a 100Ah car battery as a 20Ah deep cycle but it would not last as long.
If the battery is lead acid the normal voltage under charge peaks at 14.4, this is considered fully charged. With the fan the voltage will go a little higher, possibly as much as 1.5v higher but it is not good practice to push the voltage as high as it will go all the time. I stick to 14.4 to 14.8 for lead acid batteries
If the battery is lead calcium (PbCa) the normal voltage under charge peaks at 14.8, this is considered fully charged.I charge these around 14.8 to 15.2v
I use the 2N3055 transistor but I know there are better ones, sucahyo will be better to advise on this.
Yes some have built battery swappers to do what you say but the problem is with the fan your charging efficiency is around 95 to 97% so you only get 95% of the energy in your charging battery. This means your system will run out of power over time.
You would need to convert the mechanical power of the fan back into electricity and feed that into the battery bank too to make it self sustaining. No one that I know off has succeed in doing this with the fan, believe me I have tried. This is because the fan mechanical power was around 20 to 30% of the input and the efficiency of my generator was only around 50% then the energy used to battery swap was greater than the generated power from my fan
I am convinced that on a scaled up device this would be possible but the problem lays with the amount of useable power we would get.
If we had a 100w fan giving 95 watts to the charging battery and powering a 15w generator we have effectively 10w of excess power. Now that is a lot of machinery and batteries just to power a 10w bulb. You see the problem?
Remember these fans are a learning tool and are not really practical for everyday power generation but don't worry 1000s of us are working on a more practical solution and we will get there given enough time.
The fan is a great learning tool, it rejuvenates lead acid batteries, it is very efficient at charging batteries, it can charge zinc carbon non rechargeable batteries (normally 20 to 30% of new) and is great for experimenting and demonstrating overunity as it charges the battery and runs a fan. the combined output is greater than the input.