I think one important aspect to see gender equality in the early teachings is also the “4 assemblies” and the “bhikkhus and bhikkhunis” teachings, and the fact that women are just mentioned alongside men so consistently and with such high frequency.
Here’s a selection of the most inspiring quotes:
My all-time favourite:
DN 16 / SN 51.10 / Ud 6.1 / AN 8.70
(Mara:) The Blessed Lord has said this: “Evil One, I will not take final Nibbāna till I have nuns and female disciples (monks, male disciples) who are accomplished, trained, skilled, learned, knowers of the Dhamma, trained in conformity with the Dhamma, correctly trained and walking in the path of the Dhamma, who will pass on what they have gained from their Teacher, teach it, declare it, establish it, expound it, analyse it, make it clear; till they shall be able by means of the Dhamma to refute false teachings that have arisen, and teach the Dhamma of wondrous effect.ʺ
‘And now, Lord, the Blessed Lord has such nuns and female disciples.
“Apart from Master Gotama and the bhikkhus, is there any one bhikkhunī, Master Gotama’s disciple, who by realising for herself with direct knowledge here and now enters upon and abides in the deliverance of mind and deliverance by wisdom that are taintless with the destruction of the taints?”
“There are not only one hundred, Vaccha, or two or three or four or five hundred, but far more bhikkhunīs, my disciples, who by realising for themselves with direct knowledge here and now enter upon and abide in the deliverance of mind and deliverance by wisdom that are taintless with the destruction of the taints.”
If only Master Gotama and bhikkhus were accomplished in this Dhamma, but no bhikkhunīs were accomplished, then this holy life would be deficient in that respect; but because Master Gotama, bhikkhus, and bhikkhunīs are accomplished in this Dhamma, this holy life is thus complete in that respect.
‘But, Cunda, if the holy life is so circumstanced, and there is no teacher who is senior, of long standing, long-ordained, mature and advanced in seniority, then in such a case the holy life will be imperfect. But if such a teacher exists, then the holy life can be perfected in such a case.
‘If in such a case there is such a senior teacher, but if there are no senior disciples among the nuns (senior monks, middle nuns / monks, junior nuns / monks), who are experienced, trained, skilled, who have attained peace from bondage, who are able to proclaim the true Dhamma, able to refute any opposing doctrines that may arise by means of the true Dhamma, and, having done so, give a grounded exposition of Dhamma, then the holy life is not perfected.
‘If, however, all these conditions are fulfilled, then the holy life is perfected.’
And yet, Ānanda, whatever monk, nun, male or female lay-follower dwells practising the Dhamma properly, and perfectly fulfils the Dhamma-way, he or she honours the Tathāgata, reveres and esteems him and pays him the supreme homage.
SN 8.12 (Vaṅgīsa:)
“Indeed, for the good of many,
The sage attained enlightenment,
For the bhikkhus and bhikkhunīs
Who have reached and seen the fixed course.
“Headman, just like the field that is excellent are the bhikkhus and bhikkhunīs to me. I teach them the Dhamma that is good in the beginning, good in the middle, and good in the end, with the right meaning and phrasing; I reveal the holy life that is perfectly complete and pure. For what reason? Because they dwell with me as their island, with me as their shelter, with me as their protector, with me as their refuge.
“Bhikkhus, these four kinds of persons who are competent, disciplined, self-confident, learned, experts on the Dhamma, practicing in accordance with the Dhamma, adorn the Saṅgha. What four?
“A bhikkhu / bhikkhunī / male / female lay follower who is competent, disciplined, self-confident, learned, an expert on the Dhamma, practicing in accordance with the Dhamma, adorns the Saṅgha.
“Bhikkhus, if any bhikkhu or bhikkhunī develops and cultivates five things, one of two fruits is to be expected: either final knowledge in this very life or, if there is a residue remaining, the state of non-returning. What are the five? Here, a bhikkhu has mindfulness well established internally for [gaining] the wisdom that discerns the arising and passing away of phenomena; he dwells contemplating the unattractiveness of the body, perceiving the repulsiveness of food, perceiving non-delight in the entire world, and contemplating impermanence in all conditioned phenomena. If any bhikkhu or bhikkhunī develops and cultivates these five things, one of two fruits is to be expected: either final knowledge in this very life or, if there is a residue remaining, the state of non-returning.”
“What is the cause and reason why, Bhante, the good Dhamma continues long after a Tathāgata has attained final nibbāna?”
“Here, Kimbila, after a Tathāgata has attained final nibbāna, (1) the bhikkhus, bhikkhunīs, male lay followers, and female lay followers dwell with reverence and deference towards the Teacher. (2) They dwell with reverence and deference towards the Dhamma. (3) They dwell with reverence and deference towards the Saṅgha. (4) They dwell with reverence and deference towards the training. (5) They dwell with reverence and deference towards concentration. (6) They dwell with reverence and deference towards heedfulness. (7) They dwell with reverence and deference towards hospitality. This is the cause and reason why the good Dhamma continues long after a Tathāgata has attained final nibbāna.”
DN 32.2 about serious practice in seclusion:
Now, Lord, there are disciples of the Blessed Lord who dwell in remote forest glades, where there is little noise or shouting, far from the madding crowd, hidden from people, suitable for retreat. And there are prominent yakkhas living there who have no faith in the word of the Blessed Lord. In order to give these folk confidence, may the Blessed Lord learn by means of which monks and nuns, male and female lay-followers may dwell guarded, protected, unharmed and at their ease?’
AN 8.29 about wandering / travelling:
(5) "Again, a Tathāgata has arisen in the world … and the Dhamma leading to peace, nibbāna, and enlightenment is taught as proclaimed by a Fortunate One. But a person has been reborn in the outlying provinces among the uncouth foreigners, [a place] to which bhikkhus, bhikkhunīs, male lay followers, and female lay followers do not travel. This is the fifth inopportune moment that is not the right occasion for living the spiritual life.