General reply (from someone biased against hopping-around trips): anytime you do single-day cat, heli or guided backcountry you will lose about an hour and a half at the start of the day to do beacon training*. Given cost and time factors (eg, how much skiing you get) this argues in favor of choosing a single, multi-day option where possible. Furthermore, any guide's level of caution is going to be much higher on day one -- there will be some feeling out for the strength of the group, how well people listen, all that. This affects quality of skiing too. If you're only there for one day, you have no change to build that rapport with a guide.
All of this is absolutely true, but remember first that the OP is limited to one week in total for both resort and backcountry skiing.
I'm East Coast skier. Some Vermont, mostly Catskills.
Unless that means a lot of Vermont tree skiing in powder, places like Mustang and White Grizzly are not appropriate for a first time western backcountry trip. By reputation and location I second the recommendation of K3 for daytrip cat skiing. And DanoT is right about Revelstoke. Don't do the cat skiing there, though you might consider a heli day with Selkirk-Tangiers. Day heliskiing at RK (Panorama) or Purcell (Golden, near Kicking Horse) are other good options. Unless you have that extensive Vermont tree experience, the powder will probably be easier for you above tree line at one of those heli operators than at a cat skiing operation which is mostly in the trees. Chatter Creek (flies out of Golden for 3 or 4 days) is the lodge cat operation that has the most skiing above tree line.
If you're going to tour, especially guided, go to Rogers pass.
This is sound advice also, but I question whether a full day of earned turns is a good idea on a trip like this. You don't want to be tired when you're skiing demanding terrain at Kicking Horse and Lake Louise or powder when cat/heli skiing. I've been going up there for 1-2+ weeks most seasons since 1997, typically with 3-4 days of cat/heli skiing included. I find it's more than demanding enough physically and I have not been tempted to do any touring on those trips. If the OP has a very high level of fitness and will not get tired from skiing different terrain and snow than he is used to on his home turf, then I say go for it. But for the vast majority of people doing something like this as a first time or bucket list trip, I would say be cautious, pace yourself and don't do something exhausting early in the trip that will degrade the rest of it.
My first trip into Calgary in 1999 was what I call the "Calgary Loop" trip, dividing the time between Banff/Lake Louise and Fernie/Castle. I still prefer the latter two areas overall to Revelstoke/Kicking Horse. That 1999 trip also included a heli day at RK, as Panorama is about halfway between Fernie and Banff Lake Louise off Hwy 93. Castle also has some cat skiing, though it's so empty midweek that there's often enough soft snow inbounds to keep me busy. I recommend the Calgary Loop trip, fairly similar amount of total driving as a round trip from Calgary to Revelstoke. I have revisited Fernie/Castle in 5 seasons since 1999 and plan to again in 2018.
