I hate burnt-on grease. It looks ugly, it's not clean, and it can make your cookies taste off. It's almost impossible to get off.
Now you don't have to use grease anymore. Parchment paper works but if I was going to buy a new pan today, I would buy a baking mat to go with it--just so I can keep my pan bright and new looking.
And new pans--they're nonstick but they are lighter, prettier and yet hold their heat. I've been baking on one for six months now and love it.
Oven temperature is still a major issue. Likely your oven isn't really 350 degrees. Get an oven thermometer so you know how hot it is today.