When you're driving, you shouldn't be able to move the steering wheel at all
, without a response from your car'* front wheels. It should feel race-car tight (especially in a good Bonneville or GM equivalent, I think
So you have to decide first if that'* the problem. Play will be noticeable at standstill with the engine running, or if it'* very loose, with the engine off. Look up how to check this, or compare it to a friends car that you know is new and tight. Excessive play at 65-70 mph is scary. Play can exist anywhere from the steering wheel, through the rack, and out to the end of the tie rods. Also, just about anything else associated with holding your wheels on, if worn or loose, can effect it. Even loose lug nuts.
Since you just got the car, a trip to a highly reputable front-end specialist would be a really great idea. (You can go over the basic things first, to the extent of your abilities and inclination, but ultimately get it checked over by a pro). By the way, a long overdue chasis lube can perk up steering. Also, when you're checking tire sizes, make sure they're pumped up to the specs on your driver'* door label.
If it'* not excessive play or oversteer, then on to other issues. Be prepared that it might not be cheap to fix, but do it anyway, if you like the car.