You need to contact the NP permit office and ask for a list of specific approved bear cans. They may list it on their web site. Each jurisdiction has different approved brands. Most national parks will rent a bear can. This actually is the best way to go unless you plan on using a bear can a lot. So you may be limited by what they rent. Here in the Sierra they only rent Garcia and Bear Vault, with a very few Bearikades rented at selected trailheads.

If you can fit the bear can horizontally inside your pack it would be a lot better. Most men's large to x-large packs do this, but not most women's packs. The Garcia is more likley to fit this way than the Bear Vault, but the Garcia has much reduced capacity and is heavy. Another gripe about the Garcia is that a cook pot does not fit inside due to the narrow opening at the top. There are other brands out there that can only be purchased on the internet. I use the Bearikade- very expensive, but the best capacity for the weight. Not sure it would be approved where you are going.

On longer trips, I actually prefer to use my old external frame Kelty (with an extension bar), and simply strap the bear can onto the extension bar on the top. This really carries the weight the best.

I find that a bear can (totally stiff) vertical in my internal frame pack is quite uncomfortable. I finally got a woman's pack that I can get it in horizontally, and it really is much more comfortable. So for me it was not the issue of the vertical bear can taking up too much space, but it's discomfort.

If you plan to rent a bear can, you still may want to go down to your REI store and see what fits inside your pack. Perhaps even rent one for a day and fill it to see exactly how many days food you can get inside.

Lots of people buy a bear can for one trip and then never use it again, so you can often buy a used one.