Smt. Shivakami,
The best mantra which was given in "upadesam" to our brahmin women was "panchaaksharee" or "ஓம் நமச்சிவாய". Of course, I hope you are aware that it has to be spelt like Om namaSSivaaya (and not as Om namacchivaaya - though in Tamizh we can only write this way.) You may chant it in braahma muhoorta, or, if there is any urgent work on some day, in the morning hours. In the earlier days our women (including my grandmother and mother) used to observe மடி and also before taking even their morning coffee, etc.
Incidentally, many people have some kind of obsession with what is called பிராஹ்ம முஹூர்த்தம் and, each one conveniently imagines (and asserts also) that this denotes some period of time between 3-30 A.M. (before sunrise) to sunrise. The upanyaasams and lectures by religious people also strengthen such (wrong) ideas.
Actually, according to our ancient astrnomy and the saastras, a day (sunrise to the next sunrise, that is, and not midnight to midnight) is divided into 30 muhoorthams. Since a day is roughly 24 hours, one muhoortham will be approximately 48 minutes, and this will also vary because according to our saastras the day is divided into 15 muhoorthams and night also into 15 muhoorthams separately. Since the duration of day time (பகல்) starts increasing from the month of சித்திரை (April-May) in the latitudes of south India, and goes on shrinking from the month of ஐப்பசி, the duration of night will be smaller during April - October and longer in the remaining period of a year. This duration of night has to be divided by 15 to arrive at the duration of one muhoortham and the last muhoortham of a day, i.e., the one which comes just before sunrise is named as "samudram" and the one preceding this samudram is the muhoortham named as brahma (and therefore called braahma muhoortham). Roughly this will be from 4-24 to 5-12 A.M.
Since the next (samudram) muhoortham is not considered inauspicious, possibly one can do pooja, japam, meditation, etc., from 4-24 A.M. onwards continuously into the morning till 6-00 A.M., or sunrise. The first and second muhoorthams of a day, named Rudra and Aahi are considered inauspicious.