If I was going to try out just one Atelier game, which one would be best?
From the ones I've played, I'd describe them like this:
Rorona: The first one on the PS3, and the first one in the Arland trilogy, and generally a pretty good introduction to the formula. It has time limits, and does a decent job of making them feel relevant without being too strict. I'd say it's a decent entry point. It does most things pretty well, but doesn't really stand out one way or the other.
Totori: The second game in the Arland trilogy, a sort of sequel to Rorona (you don't have to play Rorona first, but there are some references). As far as gameplay goes, this one is pretty great. You basically just get an open world to explore, and basically everything you do gets you points that are then used to grade you at the end of a three year time limit. It's very open ended, which great, particularly as most other Ateliers are pretty rigid and linear in their structure. This sort of gameplay also helps fix one of the franchises biggest flaws (the super easy difficulty), as you can just skip ahead to the harder areas.
But there is a big problem with the game. It's filled with the sort of anime pandering garbage that makes it very hard to actually recommend, and usually isn't even part of the franchise. For example, one of the first party members you get basically does just one thing: sexually assaults everyone around her, including the protagonist (who is 14 according to the wiki, but looks and acts closer to something like 10). Constantly. And the game tries to present it like it's supposed to be funny. There's also a couple of event images that would probably give me a ban if I posted them here. In the grand scheme of things, it isn't really any worse than what you'd find in a lot of anime and anime video games these days, but it's enough that I can't give it a recommendation. Particularly since the rest of the franchise is generally free of this sort of garbage. I've also only played the PC remake of it, which from what I understand was originally a Vita game, so it's possible the original PS3 version isn't as bad.
Escha & Logy: This is one of the most polished one I've played. Atelier games in general feel sort of like budget games, but this one does less so. I can't really recommend it though, because it's just way too easy. The combat is a joke, and the time limits are super lenient. You'll probably solve all the missions the game gives you in every evaluation period in a couple of weeks, then spend the rest of the time just sleeping to pass the time. And still get all of the endings on the first try.
Sophie: Since the time limits in the previous couple of games were such a joke, the first PS4 game in the series just decided to get rid of them. And it benefited the game greatly. What you get here is just a freeform world to explore at your leisure. It's also the first game to introduce difficulty levels, and it's actually decently challenging at the higher levels, which is rare for the franchise. If you want something challenging and combat focused, this is the one to get.
On the other hand, the removal of time limits does mean that the time management aspect that previously defined the series is gone now, so this is a very different game to the rest of the franchise.
Firis: This could have been such a good game. It gives you a large open world to explore (that isn't just segmented into super small areas like other Atelier games), there's a ton of content, and the difficulty levels from Sophie are back. It had so much going for it.
Unfortunately, it's just super broken conceptually. The game is basically split into two parts. First, you have a 3 year time limit in order to complete an alchemy exam. During this time, you can explore the entire world, but a lot of story and events are just locked out to you for no reason. After you complete the exam, you are returned back to the start, and only then things like quests for your party members get unlocked. So basically you have to complete the entire game once just to get the full experience. And the actual time limit is once again a joke. I took as long as I could and explored everything, and was still done with the exam in 6 months out of 3 years.
The game also really struggles with the open world aspects. This is the first time the franchise actually gave you large open maps, and it can't quite handle them. So there's plenty of bugs and performance issues. It just feels rushed and rough around the edges. I wouldn't really recommend it.
Lydie & Suelle: This one is a lot more linear and story focused then the rest, and as a result I just feel like it's missing most of what made the franchise special and just turns it into a standard JRPG but with some crafting.
Mana Khemia 1 and 2: So this two aren't technically called Atelier, but they're still a part of the franchise according to the way the official developers number the games in the franchise. If you can handle going back to the PS2, they have a lot going for them. I'd say they're the most well rounded of them all, and also don't feel quite so much like budget titles due to the fact that they aren't 3D.
They are, however, also pretty linear and don't really have strict time limits. So like Lydie & Suelle they feel closer to a standard JRPG, just not quite as much.
So basically, I'd say:
If you want a gameplay focused on crafting and time limits: Rorona
If you want something focused on challenging combat: Sophie
If you don't mind a super easy difficulty: Escha & Logy
If you want something all around polished and don't mind going back to the PS2: Mana Khemia