As someone who's created transformative fair use fan works (aka 'rom mods') for older games as well as mods for semi-newer games (FF12), I feel that I have a bit of perspective to offer here.
There are several choices but here are the ones that stick out to me:
-Make a fan game but have it be non-profit; know that it will go poof if the copyright holder gives a damn about it.
-Make an original game and have it be completely ignored in the absolute glut of great games coming out now and in the near-future. Be lost in the crowd and lose all motivation for being 'noticed' by senpai or otherwise.
-Make a non-profit free modification of an existing game that requires that game in order to work; realize your work won't ever be standalone but do it for the love of the game.
I chose the 3rd option but my most notable/useful mods have to be the simplest ones. I created a 'bug fix' patch/mod for Chrono Trigger (SNES) and a 'Cutscenes Unleashed' mod for FF12 that removed some black bars/crap that Squeenix left in during the PC port.
I'd love for more people to make original games. For example there's an absolutely jaw-dropping amazing rom mod called Metroid: Rogue Dawn. Completely original character very loosely based on existing IP; completely original environments, storyline, and all that. Change some names and it would be an amazing indie game. But nope; they not only insisted on making it a rom mod but also on having the actual name just be a subtitle under the Metroid brand. It got some initial buzz but died off shortly thereafter because other games come out all the time. Effectively it was some glorified fanfiction but NONE OF THAT MATTERED because the actual gameplay was just so damn good. You could leave out all the story and none of it would matter!
There were some other games, one of which was the 'Dragoon X Omega' series by 'SliverX' (yeah I know) but outside of the really terrible naming scheme, they never bothered to port the game ideas and story stuff to any other platform. Bit of a shame :(
My honest advice is to just grab a game engine and mess around with it. Try a bit of everything. RPG Maker, GoDoT, Unity, whatever. Make some prototypes and demos of stupid little trash games and bit by bit you can grow it into something amazing and worth releasing. Do all this on the side and then do a crowdfund to turn the prototype into a full game. If funded, proceed to release. If not? Keep it as only a hobby.
The easiest and quickest way to money in the current age is to hire an artist and make a clone of yet another gambling-focused 'gacha' game aimed at the JP/KR/CH markets. Or do even less by buying up some cheap patents and suing people in Texas courts, lol.
That said though, you will have the easiest path in having the ability to do what you want how you want with as little friction as possible. Biggest issue with rom modding is the need for external tools/editors (or coding some yourself) while fan games face the copyright issues. There's a copyright on Pokemon but zero copyright on the idea of capturing wildlife and making them fight each other in battles.