If you google "teenage mutant ninja turtles", you get about 90 different kinds, and it can be... a bit much to try and sort through. Considering the weird back-and-forth I had to do to know what was going on, and the subsequent callers asking me what exactly is going on now that I've figured it out, here's my guide to going through it.
First off, you do not need to read the comics first or watch the movies in a certain order or anything like that. Each iteration of TMNT stands alone, and while knowledge of the other ones will help you pick up on fun callbacks and predict some events, it's not at all necessary.
If you just want to read the comics, start with the ones by Mirage Studios, then IDW Publishing. This can get even more confusing than the other stuff though, so I'll add a complete guide later.
If you only want to deal with one show, I suggest you watch Rise of the Teenage Mutant Ninja Turtles, currently airing saturdays on Nickelodeon.
TO START OFF:
Watch the 2012 series (the CGI one from Nick). A lot of people will say that this is the worst iteration of the turtles ever, for reasons that are absolutely bizarre, but in my opinon it's the most 'central' show. There's a lot of comedy, and it can definitely get goofy at times, but it also has a very engaging and occasionally quite serious plot. This series has 4 seasons split into 2 arcs and a final fifth season titled "Tales of the Teenage Mutant Ninja Turtles". The only associated film is Half-Shell Heroes: Blast to the Past, a 2D animated movie aimed at a much younger audience.
NOTE: Liked that rabbit guy in the last season? That's Miyamoto Usagi, the main character of the Usagi Yojimbo comics by Stan Sakai and currently published by Dark Horse Comics. An animated series is also in production.
STEP TWO:
Next up is the 2003 series from 4Kids Entertainment. This one is widely regarded as the best, mostly for reasons that have nothing to do with it. I do think it's good, though. 2003 is the much heavier show, but there are plenty of silly episodes too. This series has 4 seasons with an overaching storyline, followed by the "lost season", which failed to be aired on 4Kids until 2008 due to its darker content. After this the artstyle changes significantly for the final two seasons, Fast Forward and Back to the Sewer. The only assocaited film is Turtles Forever, although Cowabunga Christmas, a miniarc in the third season, is often formatted as one.
NOTE: If you're going to read the comics, read the ones by Mirage Studios after this.
BREAK TIME:
Now you get to relax and watch a movie! Actually, it's 6 movies, so maybe not. My recommended order: Teenage Mutant Ninja Turtles (2014), Out of the Shadows (2016), TMNT (2007), Teenage Mutant Ninja Turtles (1990), Secret of the Ooze (1991), Teenage Mutant Ninja Turtles III (1993). TMNT can be hard to parse, so bring a friend to that one.
NOTE: The order you watch the movies in really doesn't matter, although mine is calibrated to balance out seriousness and comedy. You can also watch them at any time, though I recommend not doing so until you are somewhat well accustomed to the characters.
THE ONE YOU SAW AS A KID:
This is the 1987 series, originally in syndication and then moving to CBS. Though considered the 'classic' turtles, the show is drastically different from the comics, focusing almost entirely on humour. The series has 7 very lighthearted, episodic seasons followed by 3 more serious seasons in an attempt to maintain viewership. Due to the low volume of content and large number of episodes, I recommend watching this more loosely, interspersed with other things.
NOTE: Now might be a good time to get started on the comics from Archie and IDW.
YES, THERE'S MORE:
Now that you've seen the main stuff, you can get started on the weird parts. From this point on it's less about wanting to watch TMNT and more about desperately calling your TMNT supplier at 2AM because you woke up in a cold sweat and NEED your fix.
Said weird parts include:
Mutant Turtles: Chōjin Densetsu Hen, a two-part anime released only in Japan that can be found fansubbed on various such websites. This is one of the most bizarre pieces of turtles media out there, and I highly recommend it.
Ninja Turtles: The Next Mutation, a live action televison series which introduces perhaps the most reviled character in TMNT history. This can be found on Turtle Dojo, or Netflix, if you want to be legal about it.
Coming Out of Their Shells, a musical tour also avaliable on VHS, and its sequel, Getting Down in Your Town. On YouTube here and here respectively (unsure of the quality on these).
We Wish You a Turtle Christmas and Turtle Tunes, two short musicals, avaliable on YouTube here and here respectively.
The shorts, including some in connexion with the 2003 series, which I have put together here.
Plenty of game, toys, and (kids') books for you to collect!
Don't forget to watch Rise of the Teenage Mutant Ninja Turtles on Nickelodeon to show them you want more turtles!
If you made it to the end of the program, good luck; all your friends know you're "the turtles guy" now, and none of you will ever forget it. Welcome to the club!