You want rechargeable batteries. Lead acid is rugged but heavy. But that doesn't matter much for a robot on flat smooth ground which sounds like what yours will be. NiMH is probably the best for you right now- fast charge, cheap, decent weight, decent power, and decent energy density, rugged, easy to charge. NiCD is similar to NiMH but much slower charging and toxic.
I wouldn't go with LiPo for you even though they are the lightest, have the most power, and highest energy density because they are expesnive. But most importanlty they aren't rugged and are finicky to charge. If you don;t use the proper charger (can be expensive) or misuse it, they can be easily damaged or explode. Yours is a ground robot anyways on flat ground so weight isn't that much of a concern.
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If the on-board computer needs 19V, you probably want 24V batteries. It's MUCH easier to step-down a voltage than to step-up a voltage.
You don't want the battery voltage to be much higher than the required computer voltage either- only high enough so that the minimum battery voltage as the battery discharges is never below the computer voltage (plus some extra headroom/margin voltage so the regulator can function properly, called the dropout voltage of the regulator). Having it too high makes it more difficult and less efficient to regulate to a lower voltage .
And because you have 24V batteries you probably want motors that run from about 24V so you can run the motor straight from the battery without regulating, stepping-up, or stepping down the voltage.
You never want to regulate motor voltages either because motors aren't fussy about the voltage as long as it's not so high it burns out the motor or so low that the motor can't produce useful work. Regulating it would make it difficult and very inefficient because motors draw a lot of current. For that reason, you also don't want to have to step-up/down the motor voltage because it woudl also be very inefficient because of high motor currents.
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We already established ~24V motors. You want gearmotors, cheap ones. Ungeared motors have enough power but its all in speed and no torque. You need a gearbox to turn some of that speed into torque to slowly turn something like wheels that needs lots of torque. The larger the wheel diameter is, the more torque you need and less RPM you need to travel at the same speed (the circumeferance is larger so you travel more in one rotation, but the raduis is larger which is like a larger lever requiriing more torque to produce the same force at the edge of the wheel).
The advantage of larger wheels is they will go over bumps and cracks more easily (but need motors with more gearing because they require more torque and lower RPM to move a certain weight at a certain speed). This isn't that big a concern for smooth ground though so for indoor robots going with smaller wheels will let you use motors with a lower gear reduction ratio which tend to be easier to find which makes it a bit more efficient and lighter too.
Look on the net or locally for cheap DC gearhead motors (motors with a gearbox already attached). You don't want to have to get separate motors and find a matching gearbox. The only real way to do that is to go to a real motor manufacturer and that is very expensive and difficult to source. Depending on the size of the robot, here are soem possible sources/examples:
www.superdroidrobots.com
https://www.robotshop.com/world
www.lynxmotion.com
https://banebots.com/
Don't forget you need a motor controller as well. A computer can make the low power signals to control a motor, but can't output the high current, high voltage, and/or power required to actually run the motor. The motor controller accepts the low power control signals and does the the high current, high voltage, high power output required to run the motor. It's like how you can't lift up a car with your arms, but your arms are strong enough to move levers that control a crane, and the crane uses hydraulic power to lift the car.
I assume you already know a robot with two fixed, front motorized wheels (with undriven, passive support wheels at the rear) where each wheel can go forward/reverse independently of the other wheel is simplest and one of the most manuevarable flat ground robot designs.
Your english is excellent.