Not how would you write an HP SI fic, where your job as the author is to make it entertaining.

If it actually happened to you, what would you actually do?

I am on team “tell Dumbledore everything and let him win the war for you before it even starts”.

Though I do have a slight concern he would view me as some sort of possession of Harry Potter and use some magic to exorcise me.

 

My plan would be to delay telling Dumbledore until the end of First Year, even if it were me in Harry's position. The time when we'd talk about the prophecy would be a good time to reveal.

My response could change depending on a few things happening the way they did in canon. Not getting the Holly and phoenix core wand would persuade me to turn in early, because I'd then know that I am too different from Harry Potter to maintain the importance of my knowledge, and the lack of protection from brother wand effect.

Changing houses would not change my timeline, funnily enough. This change, while important to later, doesn't affect the story much in first year. Hermione would still probably be friends after I rescue her. She's frankly good at magic early, and played a large part in keeping Harry alive in canon.

I'd fold early if Snape seemed to cotton onto me and starts showing changes in behavior from (presumably) reading my mind.

 

I would also be on team tell Dumbledore everything. Voldemort would be very easy to defeat if you knew where all of his horcruxes were in the first book. The power he knows not would just be your bizarre knowledge of the future. I don't know how I would present my information to Dumbledore though. Would I pretend to have some special insight because of the scar, masquerade as an older Harry, or just fully come clean. He would probably find out one way or another.

One thing that has always bothered me a bit about peggy sue fics is that the Harry often makes friends who are his physical age, while being anywhere from 17 to 100 in reality. I can't see myself actually befriending children if I went back in time. I would probably seek out friendships with professors/older students, learn as much about magic as I possibly could, high tail it out of Privet Drive as soon as it was safe to do so, buy a nice house at 1991 prices with some of my mountain of gold and put a fidelius on it so that I wouldn't have to pay any property taxes for security. I hope that Dumbledore would have no problem endorsing and or facilitating something like that if he knew some or all of the truth. If not, polyjuice potion, or some sort of non wand based disguise might let me bluff my way into legally buying a house as a child from a muggle estate agent without triggering the trace. I'm not 100% sure how that would actually work legally speaking.

In the long run, with Harry's famous name and resources, I'd probably try and get into politics.

 

I am reasonably certain that there is no way I could convince Dumbledore that I know everything because his universe is all a work of fiction. If he read my mind, he would think the whole thing was a false memory charm, somehow, not that I'd blame him. Then, I'm under quarantine while an investigation into my background seeks out who could have cast a false memory charm, which must not count as harming me. I know I don't trust myself to handle the horcruces and not go insane, so the first step is to be a cute little academic genius and get handed a time turner as soon as possible, which I assume does not actually change the past, but at least gives me a few chances at most things. It can't be that hard to dig up Riddle's bones and burn them over Christmas holiday; I'm sure the Dursley family would not have a problem with my 'running away'.
"Can I have your rat, Ron?"
"Oh, did you not know it was common to eat rats in Muggle families? I only bit the head off; you can have the rest if you like. No? Oh, well, more for me."