You can use a business to own machine guns, but the problem comes in whenever you decide to dissolve the business, sell it, retire, anything that changes the status of the business. The guns stay with the business as an asset, unless you transfer each and every firearm/suppressor/whatever to yourself at a cost of $200 each and about 6 months' wait for the paperqork to complete.
I'm also a Texas resident and I went the trust route. It's private, no state forms to file every year, and I never have to worry about naming a friend or relative as a co-owner or officer of my business.
If you want to go the trust route, which I'd recommend, try over on Texas Gun Talk forums where there are several Texas attorneys who can help you set up your trust. Don't try to do it yourself using some internet fill-in-the-blank form. Check out the attorneys. I used one who charged me for the trust and emailed it to me, and then he won't answer emails from me. Nice guy.