So I'm not going to give some backstory or anything because I don't really know his full backstory except for the fact that he was experimented on.
Why Yamato?
Because he was experimented on and ended up gaining Mokuton or better known as Wood Style. So instead of some bullshit OP gifts from God, you could have the MC wake up as Yamato after the real one died from the experiments and their souls bonded or some shit like that.
Yamato is around 4 years younger than Kakashi but you could adjust the age and have him be in Kakashi's Generation.
Also, instead of joining ROOT, you could have him just join the academy.
(A 5 man team of Minato, Kakshi, Rin, Obito and Yamato would be fire not gonna lie)
Having the wood style, the hokage would allow Yamato to look at the 1st Hokage's wood jutsus (You could also make your own)
(It would also be cool if you made his wood style more powerful because if i remember correctly he wasn't able to use the more powerful wood style jutsus)
Kyuubi attack is up to you, personally I think it would be cool if he was able to save either both Minato and Kushina or Just Kushina resulting in Naruto not being an orphan.
(I think Minato being killed would make the story go closer to canon meaning easier time writing the story but do what u want)
You could have Yamato become a Jonin Sensei of Itachi's team?
You could have the MC do something about the Uchiha Massacre (But pleass don't give him the sharingan, it gets boring seeing MCs with both woodstyle and sharingan.)
Im sure all of you know the story so i dont need to tell you what happens after that...