What's really important is handwriting itself. Block letters are honestly fine.
Writing in a good cursive (like the Spencerian script) is a bit faster and much easier on your hands, as you don't have to lift the pen as often. But that matters only when you need to write pages and pages of text.
My native language is Russian, and in Russian schools cursive was mandatory. Writing in block letters was seen as a sign of illiteracy.
I started learning English as a foreign language, and we didn't bother with cursive. So I kept writing in block letters for quite a while. I then started learning German, and our teacher taught us German cursive handwriting. I'm now using it for English as well :)