I want to power a 12V dc motor, the continuous current consumption could be up to 20A, but the peak could be 41A too. The power source's weight isn't a problem. It would be great if the motor could run for at least an hour continuously, but the more the better.

The most important aspect is the price, it would be the best to find the cheapest solution.

I was thinking about a motorbike battery, but i'm not familiar with those yet, so i wanted to ask you first.

 

A motorbike battery will not be big enough.
Try a car or better yet, a truck battery.
Look at the battery Amp Hour rating. A 40AH battery will supply 40Amps for one hour, 20 Amps for 2 hours...
But you need to make sure you do not run the battery completely flat as that can damage it.
Lead acid batteries, as from a car, are readily available and so are the chargers.
That would be the easiest track to go down.

 

Some lead acid batteries are made to be kept charged all the time (like car batteries) and are made to cope with deep discharge (like caravan batteries). The former are cheaper, the latter, unfortunately, is what you would need for this application.

Alternatively you could use a lithium battery but I suspect this would be a good bit more expensive than lead acid.

 

Here's a thread I posted that may prove to be somewhat similar to your question in that I too am looking for a PS that can deliver the necessary amperage. If you have no problem using a car battery then go for it. Just remember that it has a low voltage limit to it. I know that sounds confusing so let me explain. If you drop the voltage below a certain point by simply drawing too much current from it and allow its voltage to drop below a certain point the battery will suffer. Perhaps not right away, but if repeatedly dropped below this point - don't ask me what that is - you WILL ruin the battery.

In my post I was at first under the misguided impression the motor drew only 6 amps. When you read that don't discount my project as being no where near the scope of yours. I later determined the blower in my project drew 36 startup amps and ran at full power at about 19 amps. You'd need a very big power supply or keep your battery, should you go that route, guarded from dropping its voltage below a certain point.

Just for schnitzels-n-giggles I have some small SLA batteries (Sealed Lead Acid) for small projects. I keep them charged because if left alone too long they will drop their voltage and begin to sulfate the plates and that will ruin the battery.