I have a Trek 7200 Hybrid with the stock 700X35 Bontrager tires. I am looking for a slightly faster tire as well as a bit thinner. Most if not all of my riding is on roads and paved trails. What would be an inexpensive option?

Here are a few tires that I found.

Michelin Dynamic 700X32
Vittoria Randonneur Tire 700X28
Continental Sport Contact Tire 28-32X700

Depends on your definition of expensive.

I just switched from 700 x 37C to 700 x 28C. I put on some Continental Ultra Gatorskins. They cost me $35 each. I love the tires, they seem to roll much faster than my 37s.

did you install those on the same rims that held the 700x37?

Yes I did. I looked up my rim width on the manufacturer's web site. Then I verified on Sheldon Brown's site that my rim width would accommodate the thinner, 28C, tires.

The tire chart I used is on this page: https://www.sheldonbrown.com/tire-sizing.html. If you scroll about two-thirds of the way down, you will find a colourful chart in the section with the heading, "Width Considerations."

I've had the tires on for a couple weeks now and I haven't had any problems so far!

Thanks a lot for the clarification
I was actually planning for the same conversion on my bike and was a bit worried...

I ride 700*28 on my hybrid wheels, Mavic A119, Bontrager Race Lite Hardcase and they work great. I have also had 700*38 tire on it as well.

*Update* I purchased 2 700X28 Michelin Dynamics and replaced the Bontrager 700X35's. I will save those for the winter months. I also replaced the tubes with 700X28-32's. I took my bike for a short ride and the bike seemed to roll faster and required a bit less effort to maintain speeds. With the different tires I was able to bump up my tire pressures from 80 to 100, so that helps as well as the slightly narrower tire.