That sounds like a pretty well rounded party to me as an alternative to the tried and tested Lightning, Fang, Hope method. In the later stages of the game when I was farming for Trapezohedrons I actually found Snow to be of more use to me than Hope and had him in my party a lot of the time. I actually found this pretty annoying as I didn't like Hope or Snow as characters themselves. When I first started taking on Adamantoise though my party wasn't quite doing enough damage per stagger for my liking but was having no difficulty pushing the chain gauge up so I switched my main Ravager, Hope, out for a bit more damage with Snow as a Commando.
With a team of Lightning, Vanille and Snow you're less likely to be in sticky situations as often as you've got the best healer and best Sentinel in your team but you will be sacrificing a big chunk of damage out. If you can be bothered when you do get a bit stronger try having Snow and Fang in there with Light and you'll see just how much damage they can actually do.
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