Which mini do you have? - look under your Apple menu for the processor that you have.
Also, the amount of memory that you have installed will help, too.
If you have a mini that is running 10.4.11, then I would expect that you cannot upgrade to the current Mountain Lion.
If you have a G4 processor, then you will be limited to 10.5.8 (Leopard)
If you have an intel processor (Core Solo, Core 2 Duo, etc) currently running Tiger, then you will be limited to Lion, at the most.
I would recommend that an older Intel processor may be a good upgrade to Snow Leopard. You don't need Leopard first. You can order Snow Leopard from Apple Online.
http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard
If you can go beyond Snow Leopard, you will need that for an upgrade to Lion. You'll also find that it is cheaper through the Apple Store, rather than purchase through some other retailer, such as ebay, etc. - and definitely cheaper than buying Leopard somewhere.
Adobe CS will likely not work, even if you just upgrade to 10.5
Adobe has a document online that shows a listing of the various versions of Adobe software that are not supported by Leopard and newer.
http://www.adobe.com/support/products/pdfs/leopardsupport.pdf
FireFox has most recent update has dropped support for Leopard, so again, Snow Leopard may be a good goal - assuming that you have an intel processor, and not a PPC G4.
The Manga Studio will be OK if you can upgrade to anything newer than what you have now.