The mini-grip is a good blade for the size, but I find the handle a bit small due to the design.
For outdoorsy stuff I'd prefer a flat grind for lateral stiffness in carving, so go with the drop-point style blade rather than the sheepsfoot (which is hollow).
I like my new Kershaw Camber in S30V, but you'd have to drop the tip a bit to make the 3" limit (which I did). Bonus is you get premium steel for your budget. (and can de-assist if you don't like that feature)
I believe Buck has a Vantage model right in your size/price range, which would be a good bet.
A Vic farmer or camper is actually hard to beat too, but doesn't optimize for blade utility.
3" knives are awesome as long as they have enough handle to hang onto.