OK< my 2 cents, a trip out west is almost something all snowmobile's should; do, the scenery is worth it on that alone!
now as for where to stay, ask yourself what you want and pick a place that meets your needs
West Yellowstone IMO< is the best place to go for a first time visit, they just have way more things to offer for a first timer out there
as for going in the park, IMO< the time I went in I highly enjoyed things, but I have been in there before the guides were required,
so if you wanted to go in the park now, you will HAVE to rent a sled and a guide to take you,
I'd say do it if you like to see sights and critters at a slower pace and just enjoy the views
if you don;t want to rent and pay, outside of the park also offers a Lot of views you can enjoy
as for taking your own sled's out there,
I have done so in the past, but to be honest from me, it was always a way cheaper deal to rent
all the more so with current fuel prices!
I personally would rather fly and save my ass from a lot of sitting in a vehicle towing thru?? unknown weather conditions, and flying gets me there faster and can just stray there longer!
since SO many places offer packaged deals on stay and ride deals, some even throw in free tank of fuel each day, get you on a brand new model sled, and many sleds to pick from, and if anything goes wrong on a sled, they give you a new one!(and I have had that happen a few times out there)
IMO< the best suggestion to do, is honestly look at all options and see what the math tells you, I'm in PA< so its about 36+ hr one way for me to drive pending weather, could be longer!
add in again fuel, toll's and time
flying just saves me money and I get to use/abuse someone else sled HAHA!
another idea or food for thought too is, if you or anyone in your group wants to TRY the OFF trail you can always rent a off trail sled and have at it
But West yellowstone area will have the most trails to ride , if you really only want to ride trails!
and keep in mind almost NO one rides out there at night, all riding is pretty much day time ONLY
trails typically get groomed every night, so each morning the trails are the smoothest!
if you visit Wyoming snowmobile tourist info
Discover eight of the best places to snowmobile in Wyoming and take in jaw-dropping scenery, abundant natural snow and Western hospitality.
travelwyoming.com
there tourist web site they (used too) have a snowmobile travelers pack, you sign up for and they will MAIL it to you that lists all places to stay, and rentals, and a current trail map to look at! I;m sure its also offered in a PDF or online viewing as well, I just used to get the real USPS mailed info each time to plan my trips!
its worth getting if you planning a trip IMO
if you DO fly in, some hotels will offer free air port pick up, as well, but not all, some times renting a vehicle is worth doing , so you can work about your time frame as to the hotels on pick up and returns, , if you have a few folks going, splitting costs makes this rather cheap too!
or I always felt is was and was worth the costs!
once in West Yellowstone, you don;t really need a vehicle, can get to everything on your sled, unless snow conditions are bad?
best of luck,