what would be the best 3 man tent for about $200

For what conditions? It would help to know in what part of the country you'll use it, in what season, at what altitude, for what length trips. Those all factor into the definition of "best."

That depends on a lot of things. If you have 3 very large men, you would probably need a 4 or 5 man tent. If you are going out in winter the answer will be "there are no tents in your price range."

"Best" means lots of things to lots of people. The only thing you specified was cost. Post what else is important to you and you'll get more specific answers.

Consider:

Ease of ingress/egress.

Vestible size, or no vestibule.

Versatility.

Ease of setting up.

Ventilation.

Weight.

Bulk.

Freestanding or not.

Durability.

Single wall or double wall.

2, 3 or 4 season.

Color. Yes that's important to some people.

And that's just off the top of my head. The best tent for me may not be the best tent for you.

Like others have pointed out, there are too many variables.
If you want lightweight, consider the Tarptent Rainshadow, but you’ll have to get it used for that price.
Also consider a 10x10 silnylon tarp, bug netting and ground cloth. However, tents are faster to set up.

To keep it under $200, will cost you in weight. I prefer aluminum frames and factory taped seams. I’ve had very good results with these tents:
1. Sierra Designs - Sirius 3, http://www.campmor.com/outdoor/gear/Product___27676WC?compare=true&categoryId=200368487 I took out some useless stuff and my packed weight comes in at 5.0lbs
2. Kelty Teton 4 Tent. My packed weight is 6.9lbs http://www.campmor.com/outdoor/gear/Product___24906WC?compare=true&categoryId=200368487


I have not tried these tents but they should work well for under $200:
3. Eureka Pinnacle Pass 3 XTA 6.5lbs http://www.campmor.com/outdoor/gear/Product___28102WC?compare=true&categoryId=200368487
4. Eureka Zeus 3 Classic Tent, 5.1lbs http://www.campmor.com/outdoor/gear/Product___24217WC?compare=true&categoryId=200368487

All of the above requires only 2 poles for fast and easy setup and they’re sturdy in wind. Besides personally owning a Teton 4 tent, our scouts have been using them (kelty) for 5 years now. And they actually still look good.

-Barry