We had a karyotype done through our regular pediatrician. It was one of the first tests she did when delays were noted at 12 months.
We didn't get FISH, which can look for smaller changes than would be visible on a regular karyotype, because FISH is targeted - it looks for specific changes that you ask for. But you need to suspect something first and test for it. If you don't have anything specific in mind, it is not useful.
We were offered a microarray test at our neurology eval. They said that it can detect an abnormality in like 15% of cases that already had a "normal" karyotype because it is a more sensitive test (but looks for pretty much the same type of thing).
We have a further appointment at pediatric genetics because they still haven't found anything specific, so this will be an even more detailed testing.
They keep testing her because she doesn't have a diagnosis yet, so we don't know the reason for her delay. Everything she has been tested for so far has come back negative. Maybe if you already have a diagnosis, they wouldn't need to keep testing you.