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My personal opinion is for you to start on 9, even if you don't plan on having much about 9. Rose is in seasons 1 and 2 of the modern era.
We can do an AU Doctor if you want. I can provide a lot of information if you need any. I have seen every episode of Modern Doctor Who, and several episodes of Classic Who.

Okay, so Rose meets the Doctor after the Time War, when he regenerates into the 9th regeneration. He's on a mission to stop the Nestene Consciousness that started with shop window dummies in the building that she worked at. After that adventure, they go to a lot of different places and, in the year 2,000,000,000, Rose and the Doctor come in contact with the Emperor (who thinks himself a god) of the Daleks. The Doctor sends her home with an Emergency Protocol. Rose looks into the soul of the TARDIS, and they become one. She, with the help of the TARDIS power, becomes Bad Wolf and she saves the Doctor by turning the Daleks to dust. When it was done, the Doctor had to take the TARDIS power away from her or she would die. Because he did that, he had to regenerate into the 10th Doctor. At the end of season 2, Rose gets stuck in a parallel universe. The Doctor burns up a sun to send a hologram to say goodbye to Rose where she admits to him that she's in love with him. He's about to admit that he loved her, too, when the hologram shorted out. Two seasons later, Rose returns and helps him take care of a situation in which the world moves locations. After that is done, the Doctor takes her back to the alternate universe with a human version of the Doctor.

My idea is that, what if a good number of the TARDIS power is still somehow conected to Rose, and it took her back to the right universe, whether inside the TARDIS or right outside of it.

Yes, you are correct. Jack was the one with the Severed Hand, which actually happened within the first fifteen hours of the Doctor becoming the 10th regeneration. I can get you more details if you want.

Well, Rose would have been off in the parallel universe. But, in my idea, the TARDIS (or some device she manages to get Torchwood of the parallel universe to create) gets her to the other universe. Completely by chance, she could land inside the TARDIS, or right outside, most likely passing out because they mention that traveling without the TARDIS tends to scramble your mind a bit.

Truth be told, I don't really care which Doctor you end up portraying. Any of them would be fine (yes, i am including 1-11), or an AU (whether an AU 11 or further). It'll only be about four months for her, though it could be anytime for her.

As for AU 11, you could totally do that. Cutting out the entire Amy/Rory/River portion of the Doctor's life would honestly be thrilling to me.

The only real reason that I don't like them is for my hatred of River. Because she married him in some paradox world, it is somehow reason for her to be breaking into the TARDIS and calling him Sweety when it's obvious he doesn't like her calling him that? Rory, I rather like, but the only reason why I'm not fond of him and Amy being in the Doctor's life is because of River being their child.... Oh, wait, you wouldn't have known that from the Doctor's Wife... wait, they did mention it. Okay, I'm good.

Anyway, yeah, I can set it up. Should I make the first post, or do you want to do something about the Doctor regenerating before he finds Rose?

Either way, I really hate River. If we have her in the rp, I'll probably come up with some really, really cruel end, which would end up in having some massive paradox occur because she has a fixed death in her future (the Doctor's Past).

Okay, for the Doctor, I would suggest him being not too out there, but still have a bit of uniqueness. I kinda want to see him as a ginger, purely because he keeps wanting to be ginger, but you don't have to do that. A lesser known actor if you decide to pick from actors. David Tennant was pushing it on the lesser known, but I think he did the best job out of all Doctors. He typically has brown or blonde hair.

By this point, the Doctor would have lost a ton of companions, including Rose, so don't be afraid to have a depressed sort of Doctor. Though, once he sees Rose, he'd probably be super happy. He's always incredibly happy to see people from his past. And I bet it'd be all the more exciting for him for it to be the person he did fall in love with. I'd say watch the last minute or so of The Parting of the Ways to get a feel for how he regenerates (if you haven't seen a regeneration yet). As of the most current episode, the companion's name is Clara. You can have the regeneration be when Clara's around if you want, or you can have it after Clara (or, if you really want, with Amy and Rory, and just forget about Clara and Angels Take Manhattan).

I have a love-hate thing for River.

Yeah, I get what you are saying, I'll find somebody, and David was the ultimate Fan-Boy turned Doctor, but yes, he really was the best, because he was such a big fan. Though I only know this from my best friend and her love of David.

Oh, I too would like to see him ginger, but they are likely saving that for his final incarnation, just so that he dies for when he dies the final time, he dies happy.

Clara dies, either in the next episode or this last episode (can't remember which one from the wiki page) and is revealed to be Oswin Oswald. Thus making the Eleventh Doctor extremely happy. Now, I could have it be where Clara has just died, but his happiness has drained away because he cannot seem to find a suitable companion quick enough, thus sending him into a deeper depression than he was before and his depression causes his reactions to be delayed and on one of his solo adventures, he dies in some way, shape or form, thus causing him to regenerate. He does make it back to the TARDIS before this happens however, so that he awakens after the regeneration in the TARDIS, and perhaps finds Amy? I do not know about that detail as of right now.