If the game is on August 31, you will want to plan your week out here after the game not prior to. That is because most of the upland bird season's that will be available that time of year will begin on September 1st. That is usually true for the Grouse and Fall Turkey seasons as well as, (for what its worth), the Mourning Dove season. Pheasant, Duck and Goose seasons usually open later, toward the end of September so you might miss those altogether. There are several opportunities for both great turkey and grouse hunting within a 75 mile radius, (roughly 1 to 1.5 hrs) of Missoula in almost every direction.
As for fishing there is no end to the possibilities from Bass to Walleye! From Missoula you are within 15 minutes of three rivers all known for producing trophy browns, cutthroats, rainbows and some bass. Be careful though because there are also native bull trout in the area and they are illegal to harvest. If you prefer lakes there are several choices within an hour of Missoula, even more within 1.5 hours. On most of these you can do very well from shore.
Both the Bitterroot and the Seeley/Swan drainages are filled with rental cabins and small motels that you can book. I don't have any recommendations for guides because I've never found the need to use one. But you can get a wealth of information at the MT Fish Wildlife and Parks website at "www.mt.gov". Just go to the right side of the site and click on State Agencies, then scroll down to Fish Wildlife and Parks and you will find whatever you might need. They have a link to apply for your licenses on line, so you can take care of that before you get here.
Regardless of what you decide to do, you most certainly will have a great time out here. Be sure to take some good Missoula Brew with you! Once again, there is no end to the possibilities.