replacement tires

I just bought a 98 Golf and I'm trying to figure out what tire would be good. I purchased the Yokohama YK420 from Discount Tire and it doesn't seem to stay straight in the lane very well and it definitely doesn't corner well at any speed, it feels soft. I'm used to an 86 Golf with Pirelli P400's and I'm surprised that a 17 year old car with 4 year old inexpensive tires seemed to handle so much better. Can anyone recommend a tire that will handle well and corner without any expensive upgrades? I think I want a performance feel in an all season, rather than a touring feel...any ideas?

I have had excellent luck with both Nitto 450s and Kumo Exta7 something or other.
Did you get it aligned after getting the new tires??? Always a must