Be sure that you can drive your Canadian rental car into the US.
The other option that you could use would be to fly to Spokane and take the overnight train to Whitefish or West Glacier and rent a US rental car there that you can drive into Canada. There is also a small airport at Kallispell MT if that works better.
There are some laws and insurance regulations concerning cross border traffic with rental cars.
If you can't get the lodging you want inside Glacier NP, try the Meadow Lake Resort in Columbia Falls. It is a very nice place.

I would always stay directly in the park. They are rustic.
Many Glacier is where I am staying in July. I would suspect that most of Glacier is already full on many days for the summer.
Glacier Park Lodge and Lake McDonald would probably be good too.
There are others on the website, but they are probably more rustic than the ones I mentioned.

www.glacierparkinc.com

Kalispell has LOTS of lodging in all price ranges and is only 32 miles from the west entrance

I flew into Calgary last August and drove directly from the airport. It's one road (rte 2) all the way. Just be careful around Lethbridge as the road makes a few turns and we ended up getting lost.

We had no trouble at all driving a rental across the border.

There's a Walmart Supercenter just off Rte 2 right after exiting the airport. Get off at 64th Ave NE. The Walmart can't be seen from the road as it's behind the Deerfoot Mall on the souteast corner off Rte 2.

You can bring anything across the border except raw meat and citrus. Maybe a few other things but in general most supplies are ok.

You don't mention when you're going, for how long, what your interest are or if you have a plan for the park.

I'm going back this August a week or so after spiro is going.

On my last trip there in August I was only there for about 3 1/2 days. We spent 2 days in Many Glacier staying at the Swiftcurrent Motor in. It's about 10 minutes (max) from the Many Glacier Hotel that's right on Swiftcurrent Lake.

The motor Inn is more of a motel and MG Hotel is a hotel. I imagine the hotel is probably nicer than the motel room though I met a couple who complained that the hotel fire alarm went off the night before and it took an hour to turn it off. I guess you can't have everything.

The hotel is where the boat dock is if you're going on the Grinnell Glacier hike. The trailhead for Redrock Falls / Fishercap Lake and Iceberg Lake hikes is in the Motor Inn.

Both excellent locations for a spectacular part of the park.

Rising Sun Motor Inn is right on the Going-to-the-Sun Road in the eastern part of the park. It's close to Wild Goose Island, Siyeh Bend and Logan Pass. Very convenient. It's also not too far from the Two Medicine area.

All of the above have a restaurant.

Most people stay and visit the east side of the park. Maybe because of the spectacular scenery, wildlife and proximity to Many Glacier and Two Medicine.

I didn't get to the west side or Two Medicine last time. I will this time.

As spiro wrote, I would always opt for staying in the park. Driving time can add up quickly.

In the west part, the best is Apgar village inn, 2 stories building direct on the lake's shore, with some family unit very convenient.
In east part, swiftcurrent motor inn is very convenient in Many Glacier area. MG hotel is nice but rooms can be small.
Rising Sun is one of our favorite especially the motel rooms(not the store motel room as they are not quiet before 10 pm and woke early).
Glacier Park Lodge is convenient to visit two medecine area.
Problem is the booking...
December is late...
For next summer, even in september Rising sun was sold out in motel rooms for days I want...I've obtained a cabin but it's not the same...
So try now and sometimes a cancellation arrived.
I try every week to obtain the motel room in Rising Sun but since today, no success...
To avoid : Belton Chalet in West Glacier(near railway...), St Mary complex(service not at top, not so clean...).
Option in west part : Apgar lodge, in woods,
Erik

West side of Park statistically has more visitors than the east side of the park

If you're there to hike, you'll definitely want to stay on the east side. We are staying at Swiftcurrent in Many Glacier this coming August. As stated above, December is late to be getting reservations inside the park. In the St. Mary/Babb area, some nice options are Pinnacle Cottages or Glacier Trailhead Cabins, but they may also be booked up. We stayed in the town of East Glacier Park at Jacobson's Cottages last summer as we enjoy the hiking in the Two Medicine area. On days we wanted to hike in Many Glacier, we made the hour drive and it was not too bad.