I would choose First Xbox. To be honest I didn't have the first Xbox as there weren't many first xbox systems in my region. (probably First Xbox didn't make a big appearance in a lot of countries at that time) Nevertheless, I appreciate its library of video games. In general I like the games of that period of time. The games of early 2000s just feel different. Moreover, First Xbox improved a lot of common things like online functionality, system OS, some features of its XBL network including Arcade service.

I've played other Xbox systems. I sometimes played my friend's X360 in early 2010s. Then had XO for a major part of XO's lifecycle. And played my friend's Xbox Series a bit, maybe for a couple of times.
X360 improved some OS and online features of First Xbox and also had a library of exclusive games including some X360+PC exclusive titles and some timed X360-only games especially in the first half of X360 life cycle.
Then Xbox One was... good enough I think. It had some issues with marketing campaign and library of exclusive titles. But I don't care too much about 1-party things in general. I usually play 3-party games. If you care about exclusive lineup, then it's obvious why you may not like XO. Also Xbox One once again improved OS and online features, added some new things like BC with X360, subscriptions, Elite Controllers...
Now about XS... I've played my friend's XS a bit and it feels like another midgen of XO. It's technically more powerful, has some (timed) exclusive games, plays crossgen games with a higher quality. But overall there's no almost any unique feeling of currentgen. Almost the same Controller, an updated Windows-like interface, many same OS and online features from XO. It's like an ultimate version of Xbox One which also plays some currentgen only games (as for today, there're many games which didn't release on pastgen) This feeling actually is not bad, just it's important to understand that there're no more edges between generations.

I've never played an Xbox Series and never owned an OG Xbox, and I haven't put in 1000 or more hours playing on Xbox consoles, so take my opinion with a grain of salt.
It's between Xbox 360 and Xbox One, the two I own. Xbox One has more games to play overall thanks to its library and 360 backwards compatibiliity. But Xbox One has less exclusives and console exclusives, and a base Xbox One (which I don't have) is weaker by 2013 standards than 360 was in 2005. One X (which I have) makes up for some of that.
360 is a largely plug-in and play device. Not many games require updates to play, and installations are optional minus a few exceptions. One thing that is unfortunate about Xbox 360 is even free-to-play games require an online subscription. Even Xbox One eventually course-corrected on that.
Xbox 360 is a more unique experience as well. Xbox One and Series X/S are quite similar to each other and have some overlap with PC.
Xbox 360, but Xbox One is closer than some think.

This is kind of a sad list, because Xbox as a brand has fallen so much in my estimation.

#1 - Xbox 360
Microsoft’s publishing efforts really exploded in the early 360 years. Heavy hitters like Halo and Gears of War, plus AA productions like Kameo, Viva Pinata, Crackdown, Alan Wake. RPGs like Fable II, Lost Odyssey, Blue Dragon, and Mass Effect. Racers including Project Gotham Racing and Forza. Also, the majority of third-party console games of the era performed better on Xbox. There was also a burgeoning indie scene. Things sort of fell off a cliff around 2010/2011 and never recovered, but before that Xbox 360 made a big impression.

#2 - Xbox
A system greatly under-appreciated in its time with one of the very best launch games ever. The original Xbox was many things at once: the Halo machine; a sort of safe haven for disaffected Sega fans, thanks to titles like Out Run, Jet Set Radio, Panzer Dragoon, and Shenmue; and the place to play big PC games on console. I still remember those hours with Doom 3, Half-Life 2, and Morrowind. Finally, it hosted some all-time great RPGs thanks to BioWare.

#3 - Xbox One
I mentioned that Xbox 360 started falling off around 2010/2011. Unfortunately Xbox One did nothing to turn the tide. Halo, the flagship franchise, suffered during these years. Overall the good and great games seemed to be fewer and farther between. Now, to be fair, the system hosted some extraordinary titles: Sunset Overdrive, Titanfall, Gears of War 4, Forza Horizon 3/4, and the Ori duology.

#4 - Xbox Series
I can’t summon a lot of great things to say about this platform. I mostly use it to play Xbox One games with shorter loading times. Xbox Game Studios seems to have completely lost its way. The backward compatibility stretching back to original Xbox is great, I will say.

XBox 360 in its early years, pre Kinect focus. Despite failing twice due to RRoD it had many great games building on to the momentum of the original XBox.

The only issue I had with 360 was the black crush due to Microsoft boosting the gamma for the entire system to make games 'pop' more. There were areas in Burnout Takedown that were almost completely black on my TV. Also some issue with the borders putting crucial HUD elements (like the current objective in Dead Rising) out of the safe screen area and thus hidden on my HD ready widescreen CRT tv. The system was made for PC monitors not for TVs at the time of release...

But that didn't take the fun away from Forza Horizon, PGR, TDU, Alan Wake, Dead Rising, Viva Pinata, Mass Effect, Kameo, Bioschock, Fable, Fez, Geometry Wars, Braid, TWD and Minecraft.

XBox One discontinued many of my favorite series and Series kinda feels pointless now :/ My least used system ever.

OG Xbox easily.

For one it still runs, unlike both of my X360s.

Two, it was very innovative. 360 basically copied the good from OG Xbox and launched early before the expensive PS3, and took advantage.

Three, great console exclusives like Halo 2 and Morrowind. MS would lose these great exclusives as time went on.

It's called not participating then, you obviously don't like Xbox so why even click on a forum where the title is Favorite Xbox console? Just to be toxic, right?

Xbox 360. So many memories with my older brother, playing games like Halo 3, Fable 2 and 3, Resident Evil 5, Gears games, so much time on Gears 2 horde together, we loved a game called The Outfit and then the games I loved playing like Banjo Kazooie Nuts n Bolts (yes, I grew up with the originals on N64 and yes, I also love NnB, sue me) Viva Pinata, Kameo, the first Mass Effect, Bioshock, so many many great memories. Ahhhhh, nostalgia.

I mean, MS had only one loved AND successful home console, so it's no brainer.

OG XB. Mostly due to nostalgia. I was of the mindset that bigger was always better at that age, so the XB console seemed amazing to me. Plenty of good games as well. The graphics blew me away vs PS2. Was a relatively big Halo fan at the time, but had halo for PC though. Never got an XB because our parents got us a PS2 eventually. Just convinced them to rent the XB from Blockbuster a bunch of times. Ended up wanting and getting a PS3 instead of 360 because of the power and potential, plus the bigger size. OG PS3 was mesmerizing. My brother got a 360.
Loved the Duke the most. Was just old enough and had big enough hands that it fit like a glove. GameCube controller was a super close 2nd.

Really?
I mean, not saying you should love the console for any reason, but for having no games? The 360?