I am not a lawyer, but my general advice is this: Fangames are pretty much never safe from the copyright holder, free or no. Nintendo in particular have killed a lot of fangames of their properties, so even if you upload to your own site you will get Cease & Desist’ed if your game ever gains traction.

However they only control the trademark, characters, names, setting, visual designs, etc. Last I checked game mechanics and general concepts are not copyrightable, so if you want to make a fangame I’d recommend the “spiritual successor” route where you take inspiration without directly copying names or designs. Done properly it’s completely legal, which means your game is not likely to get sniped by Nintendo’s legal team and you can develop it in peace. So while I’d avoid the phrase “pocket monsters” (I’m not sure if there’s a trademark on it too or not), your second idea is fine.