There is a lot to do, lake fishing, trout fishing in the river, kayaking, tubing the river in the summer, hiking, wineries, breweries, petting zoo, go carts; I could keep going...

You can advertise no pets which will eliminate most people and just deal with the few that do reach out. 

As a landlord, the simplest way to avoid this problem is to just... allow pets. 

It was down to our unit and a competitor unit, so when I explained to them how pet rent works in Colorado (max of $35/month total), they decided to move forward with us.

You seem very green, I would highly suggest finding a property management company to do this for your while you learn the ropes and how things work.However, you can also get a copy of "The Book on Managing Rental Properties" by Brandon Turner, and get some really good information.The main one's to consider are:Background check - totally clear, or will you allow certain thingsEviction history - totally clear, or will you allow if no evictions for last xx yearsIncome Requirement - usually 3x the cost of rentCredit History - totally clear, or will you allow certain thingsPets - yes or no, size, type, number of pets allowed, extra pet deposit/feeAgain, I highly suggest a property manager to assist you with this.

Adding filters on Airbnb that are always targeted (are you pet friendly, do you have alt text on your pictures to hit more categories, maximizing number of beds, certain amenities like sauna/hot tub, etc)3.

On the other hand, you may do better by allowing pets and requiring pet rents, pet deposits and pet fees.

Are you pet-friendly (this will knock out 50% of your midterm rental competition).

Tenants are allowed prior approved pets.  

Consider all the things that could go wrong and see if the lease addresses them: unauthorized pets or tenants, early termination, security deposit, lease violations, late rent, eviction, lawn maintenance, parking, etc.5.