The first search in our Search Central (Enterprise Search) is very slow (in the range 10-20 s). Is this how it should be, any hints for speeding this up?
Give us something we can work with, like:
In addion to that you could tell us what the search administration reports says. You can find them in the Central Administration -> Monitoring -> View administrative reports -> Search administration reports.
10 to 20 seconds per search?
That is NOT how it should be. Even on slow hardware you should be able to get sub second results.
The first thing to do is check the Query latency reports in Central Admin. Here you will see how long it takes and where your bottle necks are. To improve search time there are several things you can do with SharePoint but really you need to find out what part is causing the delay.
Here are some hints: