This topic has been well covered, but here goes anyway.
Open sights, first shot counts in the brush, so action isn't paramount, try a win 94, Ruger carbine, Ruger frontier, as I am partial to bolt action, or anything that handles well for you. Something that points naturally, quick to shoulder, and you shoot well, it could even be a shotgun with buckshot. Just be sure to use a firearm that you like, fits well, points naturally, and you are comfortable and confident with.
For the thick stuff and whitetails, I use either a model seven is 7mm-08, or a #1 in 7x57, or a Ruger carbine in 44 Rem Mag, as all three work very well for me when fast, close, and accurate within 50 yards matters. I just pick one I feel like using that day and go.