I've read through many topics on how not to start the main quest - I DON'T give the Dragonstone to Farengar, correct?

But I have to go back and talk to the Jarl, right? I read something about not going with the female (forgot her name) to the west side of the city? I'd just like some clarity.

Can I buy Breezehome without bringing on the dragons? And how...

The Jarl lets you purchase Breezeholm after you complete MQ: Bleak Falls Barrow. He tells you just before sending you to the Western Watchtower in MQ: Dragon Rising. The dragon shouldn't appear until you get there, so maybe?

Yep. Right after you complete Bleak Falls Barrow talk to the jarl, but only about your completion and the house, then speak with his right hand man (forgot name). Then buy what you want from "guy" and avoid them like a disease.
So yes, you have to start the MQ, but you can obtain the house before bringing dragons into the picture.

Thanks a lot.