I'm a huge fan of FF7, and I did like Remake somewhat.  I thought the change in the combat system was great.  What I didn't like is how it completely butchered the original story.  If you've only played Remake, then there will definitely be parts of the story that are good, but what you probably don't realize is that all of the good parts come from the original game, and the original game has about 5 times the amount of story content that Remake had.

As for what FF game to play next, the best ones are 4, 6, 7, 9, 10 and 12.  If the old school graphics bother you, then you can skip to 10.  Both FF10 and FF12 have modern versions of the game on PS4, XB1 and Switch.  Final Fantasy was really at its peak during the SNES, PS1 and PS2 eras though.  Lots of long time fans, like myself, have kind have gotten disappointed with the games from 13 and later.

You've been living under a rock for so long. Glad you finally played it.

Something tells me you haven't completed XIII :PP

Good for you, FF7R is fantastic and I think its a very good entry point for the franchise. The combat is great, however it became "divisive" is beyond me, I have played almost every FF game there is and FF7R's combat system is probably my favorite. 

As for what to follow it with, the easiest recommendations are 7, 8, 9, 10 and 12 since they are available in current consoles, but I'd say ignore that and play 4 and 6 first, and if you feel like it even 5, you could... ehem, emu- play them in PC. There are common tropes/elements repeated throughout the franchise, and personally I feel playing the early entries gives a better appreciation when they are adapated to the latter entries. I'd ignore 1 and 3 because they are the most generic and by today standards I'd say they dont stand out particularly well, and FF2 is the absolute worst. Dont even bother with it. 

After that I'd go 7, 9, 10 and 12. In between give 8 a chance even if its junction system it uses is massive crap. 10 was the first with voice acting so keep in mind it has aged very badly and the dialogue as a whole is very cringy throughout  the whole game. I'd say leave 13 and 15 last, not only because they are the most divisive, but because I feel their characterization and story are rather weak IMO, I personally get very stressed with the writing and characters of 13. 
But bad points aside, they all got virtues and I wouldnt say any one of them is a legit bad game... except for FF2 maybe. 

Havent played 11 or 14 so I cant say much about them, but FF14 seems to be very popular 
At the end of the day everyone has very particular opinions when it comes to this franchise, its usually very divisive, so, you know, you gotta try them all. 

Long time fan of the series here (I got FF1 with my NES back in 1990). As has been mentioned, the series has some pretty passionate fans and the favourite for one person could be the worst for another. I'll just repeat what a few have said and say the FF7 Remake was a fantastic game and how they did the combat system was pretty amazing. If the series moves forward with no turn based combat, I think FF7R is what they should be basing their combat on going forward. People have different opinions on the story. I thought it was fine and doesn't destroy the original.

Now to the meat and potatoes. I'm definitely a fan of the turn based combat games the most. Mainly the ATB games. Plus FF12, which felt like a bit of a Knights of the Old Republic combat system. My personal high points of the series are FF1, FF4, FF6, FF7, FF9, and FF12. The first game is of course pretty dated and unforgiving, but this is not the case in many of the remakes. The PSP version would probably be the place to start with that one. FF4 is where we really started getting that Final Fantasy story and characters, and I think that was ultimately perfected with 6 and 7. 9 was a great throwback game to the fantasy beginnings if the series. And FF12 was a really fun and rewarding open-ish rpg compared to the very linear FF10. Low points in the series for me are FF2, FF8, FF10, and FF13. FF15 I found fun, but like was mentioned before, it felt unfinished and rushed especially near the end. I have not played the DLC.

So I recommend any of these to jump in

FF4
FF6
FF7
FF9
FF12
... And Chrono Trigger, which is basically a Final Fantasy game, released when Square was on top of its game.

Well, I'm glad you liked FF7R. If I had got into the series based on that game I would have been highly unimpressed personally.

I didn't say he did. I said it has his stink on it. Directly or indirectly the story changes smell like his garbage. Even WCW in 1998 had Vince Russo swerves a year before Vince Russo arrived. Don't have to be involved to have that stink.

FF7r Intergrade is on my list to play. With that said, if you're asking about FF15; I just finished 3 chapters (or 4?) and I must say; this is one hot piece of garbage. Is there anything great about this game?

The combat could've been good if you didn't have to fight the camera the whole time; worse yet; I find myself in closed spaces a lot of the time which makes the camera problems x100 worse. These camera problems make a lot less sense when you find out that the flashy action of the combat is automated for the most part; you'd think that would help them make the camera work better as most of the action is pre-calculated but NOPE!? WTF.

The story is disjointed; you know just enough to know what's going on but it's hard to be involved in any of it. Not even the main cast feels invested in its own story. The driving segments are slow as hell. Graphics aren't that great either; what PS4 game doesn't look good enough anyway? the amount of pop ins I am seeing on the screen is laughable. Mind you I am playing the Royal edition on the PS5 no less. The characters designs are all over the place, no cohesion whatsoever. It's like someone was making a salad but never decided if they wanted a salad of veggies or just a fruit salad so they just kept on chopping both. Awful experience, I don't think I am gonna continue playing it.

Don't play FFXV, it's terrible.

I'd suggest playing the OG FFVII just to give you an idea of what is the basis for FFVII:R and also to get the full story. Then I'd either go with FFVI or FFX two other stellar entries in the series. FFIV is also fantastic but quite short by RPG standards.

Mystro-Sama, while i will not argue which version is better i will recommend you to check other entries like they do in the comments: 

or also play the original FFVII, why? mostly because while the new Remake is a good game, it really is a new thing that's mostly its own thing and really isn't representative of how the Final Fantasy games were, even againts the original VII they are basically two completely different games. From the older ones Final Fantasy VI is the one that is constantly considered with the best story and villian in the series.