If you plan on keeping your shots within that range, then I would stick with a fixed scope. You can get a better quality fixed scope for the same price you can get a variable power one. Second you can buy a lower priced scope because the biggest problem cheaper scopes have is the optical quality at higher zoom levels. Well thats the second biggest problem cheap scopes have, the first is floating crosshairs.
I would go with one of these.
Sightron SII - These are the best scopes I have used for the money. You will have to spend much more on Leupold to get the same quality.
They make a SII in 4x and a SII Big Sky in 6x, you should be able to pick either up for around 200. Welcome to the Sightron Precision Riflescopes, Binoculars and Sighting Scopes product pages. Welcome to the Sightron Precision Riflescopes, Binoculars and Sighting Scopes product pages.
Burris is another good choice but I dont know if they make a fixed scope in their Signature Select or Diamond series. I would not recommend getting the Fullfield line, they just arent as good.
Another option since you want a fixed power scope is
Super Sniper SWFA Riflescopes Super Sniper Rifle Scopes
The lowest power is 10x and thats probably too high for the range you are talking about, but they are supposed to be the best value by far. I havent ever tried one, because I have not needed a fixed power scope. When I do, I will for sure give them a try, based on all that I have read about them.