Hi Jan,
Welcome to the forums.
A lot depends on what you want to do with it. What sort of things are you interested in? Observing mostly? Photography?
In brief ...
Alt/Az mount- Moves vertically and horizontally (altitude/azimuth)
- Can be motorised to go to an object in the sky
- Straight forward to use and very easy to come to grips with
Equatorial mount- Moves the same way the stars do (i.e. rotates)
- Can be motorised to go to and follow and object in the sky
- Needed for longer exposure photography
- Bit more complicated to come to grips with
- More expensive
Cheers,
Af.