Start problems

Hi,
when I start my baby, whether warm or cold, the starter rotates loosely up to 3 seconds until the engine starts.
After that, the engine run is immediately round, it takes great gas, does not swallow, - everything is optimal, except for the toad when starting.
Do you have any idea what I could start with when I'm looking for a mistake?
Oh yes, if I stop the start process after 2 seconds and then press the starter again, it starts immediately!
I thought maybe the petrol pump was spinning (singing sounds) or the filter was leaking (according to the motto: First of all, it takes a few turns until the fuel arrived where it was supposed to go) but as a layman, it might be too easy to think of...
Now I had the following: Change spark plugs, air filter is new, if necessary. Then replace the petrol pump.
Does anyone have any other, better ideas?? Thank you for your help,
Marius