87 Corolla starting problem? - PLEASE HELP

Okay so I just bought this car so this post might be a bit hasty, but, in the morning I go and start it up, which it does fine, but as soon as I push the gas pedal, no matter what gear, it sputters, then stalls. (It's an automatic) Is it because it's an old car and needs 10 minutes to warm up? Or am I doing something wrong when starting it? Eventually, after a lot of reving and sputtering, it starts and then drives fine. I do notice it dies a bit when I push on the gas while driving, then almost, jumps back to life.

That also happens when I turn left and push on the gas at the same time, it only happens when turning left, but it just about dies and when I correct the steering wheel and let off the gas, again, it almost jumps back to life.

Are these connected? And help greatly appreciated?

I'm assuming you have a carburetor in the '87. If so, check the float. The carb may need a thorough cleaning.