Unlike many of the guys here I prefer higher powered scopes. I've really gotten away from 3-9's, although my main hunting rifle does still wear one. I think it's mostly a personal preference. To me something in the 4-16 or 4.5-14 range is nearly perfect for hunting. I can zoom in for long range situations, but still zoom out enough for close shots. I almost never turn my 3-9 below 4x anyway. To me once you start getting the minimum magnification over 5x though, it's way too much for close range hunting shots especially if the animal is moving. In the area I hunt, the shots presented are often at running deer. If I was in a stand watching deer that weren't moving I could likely deal with a higher low end power and be just fine.
That said, if you can expand your budget a little, the SWFA SS 3-15 would be nearly ideal imo. I've been considering replacing the SWFA SS 3-9 that's on my main hunting rifle with one of these, but I just haven't done it yet. It's got the low end for close shots, but still enough magnification to be useful at longer rangers. Plus it's got reliable repeatable turrets which is the most important thing in a long range scope.