who chose/started nitnem banis?

Thanks for the question. Since it’s related to historical context, the answer can vary from one person to another.
There has been an indication in the Vaars of Bhai Gurdas that during the last days of Guru Nanak at Kartarpur- Jap baani was recited in the morning, Sodar & Aarti in the evening:
ਬਾਣੀ ਮੁਖਹੁ ਉਚਾਰੀਐ ਹੁਇ ਰੁਸਨਾਈ ਮਿਟੈ ਅੰਧਿਆਰਾ।
ਗਿਆਨੁ ਗੋਸਟਿ ਚਰਚਾ ਸਦਾ ਅਨਹਦਿ ਸਬਦਿ ਉਠੇ ਧੁਨਕਾਰਾ।
ਸੋਦਰੁ ਆਰਤੀ ਗਾਵੀਐ ਅੰਮ੍ਰਿਤ ਵੇਲੇ ਜਾਪੁ ਉਚਾਰਾ।
ਗੁਰਮੁਖਿ ਭਾਰ ਅਥਰਬਣਿ ਤਾਰਾ ॥ (ਵਾਰਾਂ ਭਾਈ ਗੁਰਦਾਸ : ਵਾਰ ੧ ਪਉੜੀ ੩੮)
Above Shabad clearly indicates that Shabad Vichaar too was part of Nitnem.
Later on, more Shabads were added to Sodar & Sohila by other Guru Sahibs. Aarti Shabad is now part of Sohila. But, the overall structure remains the same, as initiated by Guru Nanak Sahib Ji at Kartarpur- Jap, Sodar, Sohila (with Aarti).
This is also clear from the compilation of Guru Granth Sahib. The first three Baanis of Guru Granth Sahib are also in the same sequence- Jap, Sodar, Sohila. The Baani in Raags (starting from Siri Raag) starts only after these three Baanis.
It is highly likely that Guru Gobind Singh Ji also administered Khande Di Pahul with the recitation of these three Baanis only. Much later, various Sampradas or Jathebandis made additions to the core Baanis. A major part of the addition was not part of Guru Granth Sahib Ji but from Bacchittar Naatak. Bacchittar Naatak was dubiously renamed Dasam Granth by these Sampradas to give more credence to their additions (adulterations). Hence various Jathebandis have various sets of Nitnem.
But the first three Baanis of Guru Granth Sahib Ji remains- Jap, Sodar & Sohila- the routine as started by Guru Nanak and as recorded by Bhai Gurdas Ji.