Total beginner here. Don't even have clipless pedals yet. No lycra either. I even ride with a backpack. I did my first ride two weeks ago. Have only had about five rides so far. All 35 mile rides. I finish in under 2 hours. I don't know if that is good. I feel like I can go much faster and longer if I had better wheels and tires. Mine seem sluggish and heavy. Should I just buy new tires? Or should I just go ahead and buy some wheels? I have a Specialized Allez with stock wheels. Had that thing in the garage for more than a year. I now regret not riding it as soon as I got it. Should I just buy a new bike? That's another topic.
Can you guys recommend some good tires? Thanks for the help.

Clipless pedals, proper clothing and ditching the backpack will make a much bigger difference than new tires or wheels.

Getting in shape will make a big difference. You can check that your tire pressure is about 100-110 psi, and that the brake pads are not rubbing.
Fitness may make you 20% faster *
Clipless pedals may make you 10% faster *
Proper cloting may make you want to ride 50 % more
New wheels may make you .01 % faster *


* These results have not been independently verified. Your results may vary.

+1. If you bought the bike new, the stock wheels and tires are fine. Just make sure the tires are inflated correctly.

If you bought the bike used, it'd be a good idea to take it to a bike shop for a tune-up to make sure everything is in order.