Accelerating/turning noise

I get this noise - started doing it when I would accelerate hard and turn (either direction), it would be like a rumbling noise with a little vibration - I thought maybe inner wheel wells rubbing but that's not it and when the engine warms up it does it going straight as well, just an annoying rumbling (sounds like excessive engine noise (exhaust, etc...) only in 1st gear once it shifts into 2nd the noise is gone. Also right before it shifts into 2nd there is a slight rattling noise that clears up when it shifts as well. This only happens under hard acceleration.
Any ideas on what the problem could be?

2002 Chevy Cavalier 2.2L, Auto, 4-door