Mk III is ambiguous... 1D Mk III? 5D Mk III?
Any EOS film body will work...
The EOS 1v would have been a flagship, an EOS 3 would be very high end, but not flagship.
I'm skimming the listings at
KEH.com and a 1v is still $500-600 for Ex to Ex+ condition. An EOS-3 is about $250.
Like the current digital bodies... the 1 series is still best (and there were several of them but the 1v was the most recent to be the flagship body) and single digit model number bodies (e.g. EOS 3) were also very high end. 2 digit model numbers were high-end/advanced like the 33, 33v, or 50 and note that in the US market these were usually (but not always) sold as "Elan" models. And just like today, the entry film bodies had 3 or 4 digit model numbers and in the US were often sold as "Rebel" bodies.
As a curiosity... why film?
Having shot film for years and years... I have no wish to return to it. Digital is so much more convenient. Darkrooms take a lot of space (I _never_ lived in a home conducive to building my own darkroom and was always doing my developing with friends who either owned permanent or temporary darkrooms.)
I only did B&W in the darkroom... I sent color out. But there's the next issue... processing isn't nearly as popular as it once was now that "film is dead" (not completely... just mostly), so labs aren't as common. The main lab is my own town is gone. There's a lab about 30 miles from me that still does processing. And then there are places where I can drop off film and they'll send it out for processing. Some labs that used to develop and print daily only do it a few days a week because they wait to get enough film to make it worth their while (they don't want to do it for just one or two rolls.) And of course the cost of film, developing, and printing adds up over time.
This is why I say... I don't miss it.
I have a Pentax 645 behind me and quite a few rolls of film in the refrigerator... I keep thinking I'll take it out shooting, but I never do. I always grab one of the DSLRs.