Mixing brands of developer, fixer, etc., is fine.
The developer is the most important chemical, so start with one that is most readily available to you. Long life liquid concentrate developers, like HC-110 and Rodinal are good places to start. Both have shelf lives measured in years or decades in Rodinal's case
. Each will have its proponents, but try and stick to one while you are getting the hang of things.
Fixer and Stop (not real necessary for Rodinal at 1+50 or 1+100) are less critical, so you can get whatever is available.
After you've got some experience, you could look at making your own developer, like PaRodinal (a Rodinal 'clone' made from readily available household chemicals), or my favourite, PC-TEA, or even Cafenol.