My short range/brush country set up is this
Rem 700 short action in 7mm-08 AI
Hart 20" barrel
McMillan Model 7 Stock
Leupold Vari X III 3.5-10 x 40
The only reason this is a custom gun and not an off the shelf model 7 is that I am left handed and an off the shelf as mentioned in not available in LH.
But, I built this gun for the exact type of hunting you are talking about, and I made it this way for several reasons. They are...
Caliber: 7-08 AI. The 7-08 is a super caliber. Accurate and high performing. I choose to ackley improve it because 1. It did not cost any extra and I hand load. 2. If I decide to make it a longer range gun, it will duplicate .280 velocities. I think any caliber built off of the .308 parent case is a super woods and open range to 250+ yards choice.
Action: Rem 700 short action. I may offend some here, but in general, a bolt action is going to be more accurate than a lever, pump or automatic. Some folks think that it is ok to sacrifice a little accuracy because you are taking close in shots, but I have found this just the opposite. I have killed several bucks under 75 yards by shooting them through small openings in the brush. To do this you have to have 1. the ability to shoot well and 2. An accurate caliber/bullet. Bottom line is the 7-08, 3-08, .260, etc. calibers have that inherent accuracy, with much better choices of accurate and performance bullets than can be had in a lever action, or even an auto or pump gun. A gun like this will almost always out shoot a slug gun as well.
Barrel: Coupling a medium taper, 20 inch barrel with a short action just makes for a handy deer rifle that is easy to swing and point when up a tree.
Stock: Choosing a rifle with a synthetic stock just makes sense to me when that gun will be subjected to briars, brush, creeks, swamps, etc.
Scope: I will disagree with several here and say that a good variable power scope in the 2 x 7, 3 x 9, or 3.5 x 10 range is best. Why because of what I mentioned under Actions. That is to shoot in tight spots, I need a scope that allows me to aim small and is of rugged quality. Also, I need the ability to use it as my binoculars in those situations because most of the time, time is of the escence and sometimes I must acquire the target, judge if its a shooter and make the shot, all in a few seconds (Now before anyone gets upset about the last statement, please understand that I NEVER look at something through my scope that is not a game animal that can legally be taken). I have found that I can (and have) shoot accurately on 3.5 power at about 20 feet, so the need to go smaller on magnification is not an issue for me.
My set up loaded with a sling, ready to hunt, weighs about 7.5 pounds. Not a mountain rifle, but not cumbersome either.
One other thought. Except for its single round capacity, an Encore with a 24 inch barrel will measure from end to end about the same as a bolt gun with a 20 inch barrel. It may be a litte heavier, but would also be handy and extremely versitle and could handle the situation you mention plus different shooting situations as they arrive.
Just my two cents,
Smoky