Hi,
I just started playing SF1 but I wonder if I should probably directly jump to SF2 in the case that the games are basically the same.

BR,
Lutz

No.
They are both excellent games. SF2 is more streamlined, but SF1 has more to explore.
If playing only one I'd play the original.

But get the cracked Amiga versions if you know how to use an emulator: better sounds and graphics, better UI, no copy protection and much easier to save.