I had Potenzas on my '93 Civic coupe, but had overspec'd the width so that they protruded just a bit (about 1/8 inch) from the bodywork. It made it look like a sportscar hiding under the sheetmetal of a daily commuter AND I never had a problem with tire skid, wet or dry. Increase the size of the contact patch and you'll increase your grip. On an Altima, slightly-wider-than-spec'd tires should really sharpen it up.
Oh, one more thing. Don't go for the cheapest tires, go for the best tires in your budget. Remember, the only thing holding that car on the road is the rubber around the wheels. Owners of first-generation Ford Explorers will attest to that.