1. For taking Mantra Diksha, Vaishakh, Shraavan, Ashwin, Kaartik, Maargshirsh, Maagh and Faalgun are the best months.
2. In Aashaadh month, except for Lakshmi Mantra, all other Diksha can be taken.
3. Kaartik and Maarg Shirsh months are best for Lakshmi Mantra Diksha.
4. Tantrik Mantra Diksha should be taken in Maagh or Faalgun months for getting special benefits.
5. Purushottam month is forbidden for all kinds of Diksha.
6. According to the Rudraymala Tantra, Kaartik, Sshwin, Vaishakh, Maarg Shirsh, Faalgun and Sharavan months are favorable for beginning any kind of Mantra Sadhana.
Mantra Diksha can be taken in any Paksh but Sadhana should be commenced only in the Shukla Paksha. Krishna Paksha is auspicious for Moksha granting Mantras.
Mantra Sadhana commenced on 2nd,3rd,5th,7th,10th,11th,12th and Purnima is very auspicious.
Beginning a Sadhana on Khachaturian, Navami and Chaturdashi is forbidden.
Akshay Tritiya, Naag Panchami, Janmastami, Durga Ashtami, Trayodashi and Chaturth Tithi of Krishna Paksh and Amavasya – all these are moderately favorable.
Swinish, Rohini, Mrugshira, Punarvasu, Pushya, Maghaa, Purva Falguni, Svati, Anuradha, Mul, Purvaashadaa, Uttar Aashaadh, Shatbheesha, Purva Bhadrapad, Uttar Bhadrapad and Revati Nakshatra are favorable.
Aardraa and Kritika Nakshatra are specially auspicious for Shiv and Agni Mantra.
Monday is moderately favorable. for beginning a Sadhana. Beginning a Sadhana on Saturday is equal to inviting death. All others days are favorable.
Vrishabh, Sinh, Kanya and Meen are favorable. Lagna for Mantra Sadhana.
Vishnu mantra should be started in Mesh, Vrishchik, Sinh and Kumbh Lagna.
Shakti Mantra can be started in Mithun, Kanya, Dhanu and Meen Lagna.
Shiv mantra Sadhana can be started in Mesh, Kark, Tula and Makar Lagna.
Keep in mind that the above auspicious timings are in general. Other than what I have specified, one must also look at Ghaat (घात) Chakra in his Janma Kundli. Ghaat Chakra is the list of Lagna, Tithi, day, direction, etc unfavourable for a person. I cannot tell anything about Ghaat Chakra because it is different for each Kundli and person. Other than this, many Sadhanas have their own special rules. If rules are not specified, the above things must be referred.