You are doing it wrong. You should not use PhotoIShouldNotUseItForLogosShop
Your logo is now limited to the fixed size you made it.
resolution/file size to save logo
This also has no sense. Resolution is not a parameter to take into account. Resolution is just a metadata on a file.
File size has no sense either. A parameter is never "a 1 Mbyte file".
will be used in an Instagram header
Here is the only place there is a specific image size. A simple google search: "Instagram Logo Size" says 110x110px.
also will be printed on all kinds of different stuff of various sizes
You need to remake the logo on a vector based program. Corel Draw, Illustrator, Affinity designer or Inkscape.