May 15th is pretty early for Yellowstone. Your choices may be influenced by what's open, rather than what's recommended. Here's a list of lodges and their opening dates this year:
https://www.yellowstonenationalparklodges.com/stay/plan/opening-and-closing-dates/ It looks like Canyon Lodge will be the only lodge that won't be open when you arrive, but will open a few days later.
Be prepared for cold temperatures. There will be snow around, but that will keep wildlife down low- where the main roads are. You will be well ahead of the crowds of Summer. Fortunately the thermal features don't shut down for Winter. Stay on the boardwalks. Watch for Bison-pies.
It's 22 miles to the entrance from Island Park Village (now Timbers Condominiums). If you want to picnic in the Park, box lunches are available at several places in West Yellowstone. You should absolutely plan a meal in Old Faithful Lodge- You'll never forget it. There is a good- though rustic- restaurant near the resort entrance- and some limited groceries across the road- at c-store prices. There are a couple of smallish well stocked supermarkets in West Yellowstone. Be sure to continue past the resort entrance to Big Spring. The Henry's Fork of the Snake river surfaces there, whole! There are gigantic trout, muskrats, the occasional moose often seen there. I doubt the Johnnie Sack cabin there will be open yet. We also like eating at the Boondocks restaurant in Island Park. It will be on the flyer you'll get at IPV.
If you are over 62, be sure someone brings a National Park Pass. It will get the whole carload in to both parks. One great perk of being a senior!
Enjoy!
Jim
P.S. There is Wi-Fi at IPV, but mobile phone service is nearly non-existent inside the parks. You might find some slow analog service near the park lodges but don't count on it.