Get an alignment, rat now. Once you start scalping or cupping a new set of tires it is nearly impossible to straighten them out. Why would you spend that kind of money on a new set of tires and not an extra $60 on an alignment? If the car wanders it is probably your toe in/toe out adjustment.
Too much toe in and the car plows (difficult to streer but goes in a streight line like a mother). Also toe in will scalp your tires on the outside edge. You can feel this by running your hand across the top of the tire backwarss towards the rear of the car. With too much toe in you will feel a 'feather' on the leading edge of each tread segment. A few thousand miles like this is enough to ruin a good set of tires for life.
Too much toe out and the car wanders and won't hold the road. Toe out will also scalp the tires (on the inside edge) but not as quickly as toe in. You notice toe out much faster than toe in, but over the long run toe in will do more damage.