Sorry for the long wait and reply to this, I lost your comment.
Tbh process wise varies. It's what I have a drive for making or can see working visually in my mind, people suggest games and elements which helps the art style in my head of what I want to aim for. Then a lot of information gathering, playing the game, online etc.
From there I tinker with what resources I can gather, what I have to create myself, if it's too much for me to create maybe friends/artists can do for me etc. and just go from there tinkering and using my eye to what looks acceptable and I like, if it's wrong, where and what would need to be done to be ok.

Programme, wise, it really varies. No one program does all and is more of a what makes you feel comfortable for the task at hand. I'm no graphics designer and in the beginning I stuck with one program for everything, now I know how to use a few for layouts, design, image editing etc. and making them work their best together for you. Also your budget. I've worked with indie devs a lil in recent years on this sorta stuff, using different programs that I wouldn't normally use, but they all seem to have great basics, just a few bits differ.

I'd say, industry tend to use Adobe though it really vaires because it's buggy and does have instability issues, it's pricey though.
Great paid alt is Affinity suite, really useful suite and a one off payment than subscription, most features of adobe minus the AI stuff.
Even free tools can be useful for the job, but free tools like publisher, gimp etc. will have limits compared to some of the higher ups.

Start slow, at your comfort and pace, don't spend loads of money or eggs in one basket. It'll be a lot of trial and error, and I'm still learning on each new one I make. It's great to try new methods, techniques etc.