We have no children. If we do a trust to protect from nursing home, what kind do we need to do?

I guess I wonder why you are concerned as you have no children, who do you plan to leave your money to?

Me, I am alone, have no children, 1 brother, I am not worried about saving my money as there is no reason to.

I'll spend it for my care in my last years, I do not want to tax others for my care, that is why I planned for my retirement.

My mom used a Certified Elder Care Attorney (CELA) to help her make sure everything was set up just so. Here's a link that has good information about planning and trusts, and a way to find local attorneys. (You may have to copy and paste it into your browser)
https://www.elderlawanswers.com/kinds-of-trusts-12007

We have a checking account for my mom where her SSI is automatically deposited. We know how much her expenses are each month, so we have the trust 'top off' the checking account with a set amount of money each month to meet her bills.

SSI + monthly trust autodeposit = monthly expenses.

Then we have her AL rent and other expenses automatically paid out from the checking account.
There's also a credit card that links to the checking account for incidental things--that gets paid online by the POA.

The bigger question is: who is going to manage that trust when you eventually can't? And make decisions in your own best interests? If you don't have someone who is at least a generation younger than you, who is local, who you trust, and is willing to do the management... you may need have to hire an attorney be your trustee, PoA, etc. I'm not sure who else can be paid to do it, and who is accountable, other than an attorney, but others on the forum will know.