Idles rough when stopped/ jumps into 3rd gear.

I just bought this car 3 days ago from a dealership. It doesn't have an exte4nded warranty, but they will give 15 days to take the car back to them with any issues to fix, so I'm trying to see if the issues I'm having are issues that need attention or if its something I can do myself to fix. I noticed the car idles rough when stopped at lights or stop signs, it idles even more rough with the ac running, but aside from that, ive also noticed when I push the gas a little harder than normal, the car seems to jump into third gear. This is the only gear that will do that, after it shifts into third, it drives normally. It is an automatic, so I'm worried about the transmission being an issue. If I'm not pushing the gas, such as accelerating onto a freeway or something, the car drives like a dream, its only when trying to accelerate quickly. Please help, I don't want to be stuck with a lemon, I have limited funds, and I would like to get this resolved before my 2 week warranty expires. Thank you