Using only the characters from the OP to determine sidekicks:
In order of sidekick roles with Bruce:
1.) Dick Grayson
2.) Tim Drake
3.) Barbara Gordon
4.) Damian Wayne
5.) Carrie Kelley
6.) Jason Todd
7.) Cassandra Cain
8.) Duke Thomas
9.) Stephie Brown
10.) Harper Rowe
In order of how I like their characters:
1.) Dick Grayson
2.) Barbara Gordon
3.) Tim Drake
4.) Damian Wayne
5.) Carrie Kelley
6.) Cassandra Cain
7.) Jason Todd
8.) Duke Thomas
9.) Stephanie Brown
10.) Harper Rowe
These lists are not entirely accurate indicators because I like some characters more in previous mantles than the ones they hold now. For instance, I like Jason as Robin but despise Red Hood. And for the sake of fairness, I won't hold characters' presence in Detective Comics against them. Otherwise, they'd all be much lower.
Tim and Damian were difficult to rank because I like Tim as Robin more than Damian (depending on the day) but he's been upshowed and worthless since Damian was introduced. There's not room for both of them. Damian slipped because of his absence in Rebirth Batbooks and his insufferability in Teen Titans. He really shouldn't be on that team.