I would rank them as....
The first two are just more interesting players to own imo. There's no such thing as a "safe" goalie pick, so I look for upside and at least signs of good development which is what Andersen and Nilsson will give you. Fwiw, Visentin is probably the most likely to have a long NHL career. but when that career is probably as a backup I'm not sure if that's what anyone really is looking for.
Andersen over Nilsson is a personal choice on my part....I own both players on my fantasy team so I've followed them as much as possible. If Andersen had signed with Carolina he would be the backup this season, and although he's splitting time with Bobkov in the AHL so far I expect him to eventually win that starting job. He's huge, and plays a blocking style a lot like Giguere
He may have Hiller and Fasth ahead of him on the NHL roster, but I don't expect Fasth to be much of a roadblock long term, his upside at this point is a backup and at his age I could see him leaving Anaheim looking for a starter's job or going back to Sweden. Hiller is 30, and a UFA in 2014. With appropriate development on Andersen's part (which I don't worry about, I think he's a legit prospect) he could very well split time or be Anaheim's starter beginning in 2014. I personally have Andersen on a tier behind Markstrom and Lehner in terms of goalie prospects.
Nilsson is a close second, and I would have no problem if you wanted to list him first. He's another big guy, in a good situation in New York. Kevin Poulin is really his only competition, and the Isles are putting together a strong young team. He showed he can handle the NHL last year although it was only a few games, picking up his first career shutout. He dominated the AHL last season after a rough start.
Like mentioned before, I'm not excited about Visentin. He could be a backup for a long time, maybe a low-level starter but I'm not sure he'll ever be fantasy worthy. And Mrazek, although an intriguing prospect, won't see the NHL for 5+ years if at all. I know you said long-term but he's very much a maybe at this point and even if he does pan out it's a looooong wait.
20 Team Dynasty (points per) - G (25, 50 for defense) A (25) PIM (3) +/- (5) PPG (15) SHG (25) OTG (15) GWG (25) HTr (50) GP (2) HIT (1) BLK (1) Use actual NHL salary
F: Malkin, Tavares, E. Kane, Parenteau, Havlat, Tarasenko, Galchenyuk, Brunner, Boyes, Kruger, Helm, M. Martin, Bergenheim, Carcillo, Stajan
D: Green, Ehrhoff, Ekman-Larsson, Coburn, Daley, Postma
G: Fleury, Mason, Montoya
Farm: Grigorenko, Grimaldi, Kucherov, D. Shore, Hartikainen, Stransky, Kerdiles, Joensuu, Pageau, Murphy, Ceci, Klefbom, Thrower, Donovan, Ekholm, Lehner, Dansk, Poulin, Nilsson, Andersen