I am looking to buy an over-the-range microwave oven.  Since I will
mostly be using this to make popcorn and such my primary concerns are:
   1) a good vent for the gas range below   -and-
   2) price

I have found over-the-range microwave ovens with vents up to 330 CFM. 
The ideal answer will point me to an over-the-range" microwave that
has a range vent faster than 330 CFM and costing less than $300.

Hello  Mrinquisitive,  

Best Buy carries an over the range microwave that meets your requirements.

This is an over the range microwave oven with 400 CFM ventilation. It
costs less than $300.00 and it?s available in black or white.


In Black

Samsung 1.7 Cu. Ft. Over-the-Range Microwave with Turbo Ventilation - Black 
Model: SMH7174BC 
 
?Take advantage of a microwave that keeps your kitchen smelling fresh
with a 400 CFM Turbo Ventilation System that quickly eliminates any
food odors.?

Price: $256.49
Reg. Price: $269.99
You Save: $13.50

Purchase here:
http://www.bestbuy.com/site/olspage.jsp;jsessionid=JM42F0B2VZ0N1KC4D3KFAFY?skuId=6282603&type=product&productCategoryId=cat05021&id=1072286882655


In White

Samsung 1.7 Cu. Ft. Over-the-Range Microwave with Turbo Ventilation - White 
Model: SMH7174WC 

400 CFM

Price: $256.49
Reg. Price: $269.99
You Save: $13.50

In Stock Usually ships in 1 business day

Purchase here:
http://www.bestbuy.com/site/olspage.jsp;jsessionid=JM42F0B2VZ0N1KC4D3KFAFY?skuId=6282587&type=product&productCategoryId=cat05021&id=1072286882602



Search terms used: 
CFM 400 over the range microwave

I hope this is helpful.

Best regards,
Bobbie7

Excellent answer.  Everything I asked for and more.