Quote:...I’m trying to make a simple logo in GIMP which I need in different formats (small logo, business card) ..
Different sizes, same quality. you need to be working in a SVG (scalable vector graphics) format using an application such as Inkscape.
In my opinion, the biz card is the best size as a base. There are pre-sets in Inkscape.
example: (this one attached) see: https://i.imgur.com/EWpjthx.jpg just a guess at the font.
Opening in Gimp, a variety of options see: https://i.imgur.com/cU7gkhd.jpg
As it will open (1) about 300 pix wide
Increase the resolution to 300 (2) for say a letterhead or send to the printer, about 1000 pix wide
Set a size in pixels for a flyer (3) 3000 pix wide.
All will scale with equal quality, just do not re-scale once opened in Gimp.