I think that "medium format experience" means they want you to know how to safely handle rolls of 120 and 220, and know how to load their cameras and camera backs. The first part can be achieved by using almost any medium format camera (maybe not the 220 part). As far as loading cameras and film backs they are all a little different, so I can't see them expecting someone to have used everything out there. They want you to be able to figure it out quickly when they show you, and to be able to trust you to load it right. Then again, you may be hard pressed to find a pro that hasn't sold off all their medium format film gear already.
If you get a deal on a 645 camera that's fine, but overall I think 645 is already a dead format. It was great for wedding shooters, but as JIP said, it's all gone digital now. That fancy, full frame, 16mp Canon DSLR is pretty much already matching 645 (check out comparisons of 645 Velvia to various digital cameras at Luminous Landscapes). You may want to consider something bigger. Bigger does not mean harder. It does mean less shots per roll, but lots more neg!!! It's worth it. Most cameras with interchangable backs can handle various format sizes. I offer medium format film photography to my clients (commercial and wedding), and they aren't interested. I use it for my personal work where film economy isn't such an issue. I'd rather have the big neg.
Don't worry about an in-camera meter. If you're going pro you should learn to use a hand held meter anyway.
If you're investing in MF, you need good glass,
mirror lockup and leaf shutter.
Doc, your points are valid, but I'm going to play devil's advocate...
Even dirt cheap, no-name, medium format glass does a fantastic job. I get great results from my $15 anastigmat lens, medium format camera. If you have the budget for Zeiss, Mamiya, Schneider, Pentax, or Fuji then go for it. If your budget is more like Yashica, don't worry about it. There are plenty of brand names people aren't familiar with that are as good as it gets. I have a Norita 66, which hardly anyone has ever heard of, and it's lenses are just as good (and faster f/2) as my big name brand lenses.
Mirror lock up is only important for an SLR. Other kinds of medium format cameras don't have moving mirrors, or mirrors at all.
Leaf shutters are nice, until you need a shutter speed faster than 1/500th. The Pentax 6x7, 67, and 67II are extremely popular focal plane shutter cameras. I love my 67II, and it does just as good of a job as my Hasselblad with a leaf shutter. Almost every photographer I've seen on TV using a medium format camera is using a Pentax 67: David LaChapelle, Spencer Tunick, Richard Avedon, Glenn Ketchum, and on and on. The people who have problems with focal plane shutter movement need to work on their technique, because their are plenty of photogs having no problems. Also most focal plane shutter cameras have leaf shutter lenses available, so it's the best of both worlds.