I would say Final Fantasy, but that IP has gone full circle in a lot of ways.

I never played GTA 1, but I did play the second.  I really liked the system where you could work for 3 different gangs, and it was sort of a rock-paper-scissors thing where working for one would increase your reputation with one gang and lower it with another.  I actually liked it better than anything I played in GTA 3.  The masses were always going to like a 3rd person from behind view over a top down view game though.

I find 4,6,7,8,9, and to an extent...10 far superior to 1,2,3 and 5.

I say it went full circle though because of 13 trilogy, and while I enjoyed 15 and FFVIIR, they are not on the level of the golden era IMO.  Never played 12, can't speak for it.

I loved 14 though, great MMO and it had that classic Final Fantasy feel to it.  The only reason I stopped playing is because MMOs are bad for me IRL, so I swore off them.

Very much agree there.  I came to the first Warcraft late, so it is probably not fair, but that game is so rough compared to other RTS games that came out just a year or two later.

Zelda.
The first two on the NES were crude and frustrating, but from Link to the Past onwards it became one of the premiere franchises in all of gaming.

God of War. Never understood the appeal in Square-Square-Triangling my way through a billion enemies, then doing toddler-level puzzles and baby's first platformer all as a character that was not tragic but just a pathetic fool who might as well have been an incel for all the responsibility he took for his own actions. The first God of War games on PS2/3/P were all faux-edgy trash...

...but the 2018 God of War was a near-perfect masterpiece of art, direction, combat, growth, maturity, and production values. It looked great, felt great, played wonderfully, and had a remarkably well-written story with equally well-written characters. Honestly one of the best games of all time to come out of the most overrated series of all time next only to Halo.

I think it goes in cycles. FF was simple but pretty decent. II and III were wholly forgettable and dare I say pretty bad. but then IV, V, and VI were all outstanding (VI is my personal all-time favourite game, with IV and V being underrated gems). VII was a masterpiece, VIII was controversial but I still loved it, IX is another masterpiece. So the first NES gen was...okay....but SNES and PS1 gens were some of the best games of all time. I personally think the PS2 gen is similar in quality, but I have a REAL hard time counting FFXI since it's online and X-2 - while fun - was a joke. FFX was another masterpiece that was missing something special and XII was a great GAME with great characters that lacked in plot and narrative (Something we see again a few entries later) 

XIII is the worst game of all time. 

XIV is another one that's online and therefore doesn't count (And didn't get good until A Realm Reborn came out)

XV is fun with some good elements but absolutely fails in terms of plot and narrative structure (while mastering interpersonal character work)

So yeah, all over the place, but everything from IV-X was an absolute masterpiece, with I and XII also being up for contention as great entries. 

The thread title asked for IPs that started as mediocre.  I never said 1,2, and 3 were bad.  I am implying they are mediocre at best.

As for 5, it is wedged in start of the golden years for Final Fantasy so it still kimd of fits the topic in a way.  The main reason I only mentioned it however is because I simply did not want to leave it out.  If I was to make a statement that 4-10 would be the golden years of FF, I feel it necessary to point out that 5 would be the black sheep of that bunch as, IMO, it did not stack up to the rest.  It is in there for clarity more than anything else, but the point remains the same.

That’s not what the thread is asking for.

The Super Mario series didn’t go from mediocre to good.

It got, arguably, dips from exceptional quality to something somewhat lesser, from one’s perspective to another. 

But it’s never ever been a mediocre series.

The first games still play exceptionally well. But if you’re a fighting game veteran, sure, its gameplay can be somewhat simplistic compared to what the genre offers now.

Being one of the fighting games I’ve played the most among all the ones I played in my gaming life, I have to disagree that they were ever mediocre. When the game came out in the arcades in the 90s (94 if my memory serves me right), it was the only franchise that managed to compete against the Mortal Kombat series. At least in America.

To this day. the first Killer Instinct is still the best fighting game I have played when rated from the day and era in which it came out.