You didn't ask for the best saw, just the best bang for your buck.... so the lowest buck item that can limb a tree comes to mind.
If you want new I'd say the cheapest tanaka / poulan / craftsman / whatever around 40cc's will do the job... try craigslist or if you are really daring go for one of those chinese clone types that don't even have a known brand name
if you want used the same brands above apply, but you can also usually score a husky, echo, or something better for less than $200. A used poulan wildthing would be great bang / buck.
Now you if you asked for the best quality for your dollar or best saw for full time use or other criteria the "quality brands" Stihl, husky, dolmar, etc might be up your alley
Don't lump all Stihl and Husky saw together Keep in mind Husky and Stihl homeowner saws have way less quality the Dolmar , Echo and Efco saws. Steve