Is it possible to control the motor speed through programming with a picaxe board? or do i have to buy the motor with the speed i want?
You can buy a DC motor with a specified speed, and run it slower in a few ways.
To reduce the speed of a DC motor, you can:
I'm not going to dive into using other types of motors, as you didn't specify which type of motor you want to drive.
I'm sure if you tell us the basic part of what you want to do we can help even more, so give us some feedback :)
Check out this tutorial. It is for Arduino but should be very similar to the picaxe.
It shows how to use an H-Bridge chip and control speed on a motor. The chip they show in this tutorial is only good to 0.6 amps (I think that is the spec on it) so may not be appropriate for your situation. If you can tell us what motor you have, what you are trying to do and what you have done so far we can give more concrete recommendations that will address your situation.
You can vary the power to the motor using PWM. Choose a motor and gear box that will give you the fastest speed you need at full battery voltage. If you have a big, heavy load then you need a more powerful motor and stronger gearbox.
Since you question is very vauge due to a complete lack of research I can only give you a very vague answer.
General rule is that you search google before asking a question.
Speed control of motors, extensively documented. PWM is your friend.