The lease specifies that my landlord must provide written notice to me at the end of my lease in order for me to be held to a 60-day notice, otherwise it only needs to be 30-days. Bottom line: what constitutes a legal and proper "written notice" pertaining to this in Texas?
Whatever the lease says. Most leases provide for where notices should be sent. If the notice complies with the terms of the lease, it's sufficient.
Ultimately, the question will be resolved by the Lease itself. If the Lease specifies when, where, and how the notice must be sent, you must comply with the Lease. If the Lease does not specify, you can use any commercially reasonable method. In such a case, I would send a typed letter stating "I, [your name] occupy unit [#] at [property name, property address]. I hereby terminate my lease effective xx/xx/xxxx." Be sure that the letter lists all persons on the lease in the body and is signed by all adults residing therein. Mail it to the same place that is specified in your Lease for payment of rent. Send one copy Certified Mail, Return Receipt Requested and send one via regular mail ($0.45 stamp). Mail them both at the same time and be sure that both have your return address on them.