ODI debuts by Indian players were highlighted in the first match, both in batting and bowling.
ODI debuts by India (minimum 40 runs):

KL Rahul is the only player from India to score a century on ODI debut. Before that, RV Uthappa’s record of 86 stood for several years.
This table also gives the strike rate for the innings. Indeed, the highest rate is 187 by KH Pandya, far ahead of the previous record of 127 by Azharuddin back in 1984-85.
This list includes several who served India well, and others who vanished quickly. For instance, Khurasiya scored 57 on debut and played in only a few ODIs after that.
Now we look at those who scored 40 or more on their ODI debut which was against India:

The highest is 90 by SP Fleming, who also scored 90+ on his Test debut. Some other famous names here include Wade, du Plessis, RB Richardson and YJ Bairstow. Others such as CS Cowdrey and Moxon did not last long.
Now we look at ODI debuts by Indian players, with a minimum of 3 wickets in an innings:

We see that MP Krishna’s 4-54 is the best by an Indian player on ODI debut, surpassing the long-forgotten NA David’s 3-21 in 1997.
David’s 2.62 is also the best economy rate here, followed by ST Banerjee’s 3.00. The worst is 6.66 by C Sharma, just ahead of Krishna’s 6.61.
Prominent names here include Pandya junior, DR Doshi and even BS Chandrasekhar.
Finally, we look at those who took 3wi on their Test debut which was against India.

The best here is 5-28 by BD’s Taskin Ahmed, just ahead of AA Donald’s 5-29. Donald and maybe Henry and Styris are the only others who lasted long enough.
The best economy rates are 2.50 by FA Rose and 3.16 by SA Thomson. The worst is 6.30 by SB Styris.