Anyway you study Śikṣāṣṭakam is good, but generally systematic study is recommended
The ācāryas also explain it systematically and relate the verses to different stages of devotional service
Lord Caitanya doesn’t speak about anything else than chanting Hare Kṛṣṇa, how we chant, what is the result, what is its perfection
Bhāg.8.23.16: „There may be discrepancies in pronouncing the mantras and observing the regulative principles, and, moreover, there may be discrepancies in regard to time, place, person and paraphernalia. But when Your Lordship's holy name is chanted, everything becomes faultless.” (Śukrācārya)
Maintaining things is much more difficult than to go out and break new frontiers
We need both, maintain and expand