Congratulations on coming to YNAB and on your husband's business plans.
I think you do need to see a tax professional until your husband gets his business established. In the meantime, perhaps googling something similar, such as "self-employed personal trainer" or some other business that can be done out of a space at home and has similar equipment needs.
My husband can claim a home-office deduction because he is self-employed as a contractor and has an office in our home. So we can deduct a percentage of home expenses such as utilities as a percentage of square footage of the house. (I have done my own taxes for three years and this past year I didn't even claim this deduction because it's a common flag for audits and even though it's legit I got scared! I'm going to see an accountant this year.
Basically anything your husband uses toward the business can be claimed for tax purposes. However, you should find out what the cutoff point is between hobby and business. I think there is a distinction based on income; you can run a business at a loss for three years or something and then after that it's considered a hobby. If he wants to consider it a business he will have to file a Schedule C. Again, I'm sure there is plenty of info online if you google something about hobbies versus businesses. I'm not sure if regular Turbo Tax has a Schedule C available or if you have to bump up to the small business level but the Turbo Tax website has a chart that can help you decide which form you use.
But I do think to get off the ground it would be best to see a professional. Good luck with everything!