Ulitmately, you are on the hook for the mortgage, if it is in your name.....even if you co-sign.
Since this is your daughter, it may be well worth the risk for the benefit that it brings to you and her.
Before embarking on this venture, outline, preferably in writing, who has what authorities and who is responsbile for what maintenance, upkeep, and expenses. I am not suggesting this be a legal document, but a written reminder in the event confusion arises at a later time. Who will fix the furnace when it needs repair? Who will paint? Who will pay? How will the allocation of the mortgage expense be paid? How much does your daughter pay? How will appreciation be allocated (assuming you hold the property long enough)?
For your daughter, unless their is a benefit to her in this arrangement (equity), she could view the arrangement as restrictive. If she is only your tenant, and you derive benefit of a built in tenant, with an asset, possible appreciation, and tax write offs, it would be advantageous to you, but perhaps, not her. Look at what makes a win-win situation.
Since this will be your daughter's home, you may want to look at newer places that will have less maintenance.
As it pertains to your finance and tax write-off questions, your advice needs to come from your accountant or financial planner who can review the whole picture for you. The answers to these questions depend upon so many factors in your personal financial goals that have to be considered.