As rlp said there are as many guns as opinions. My opinion is this, simply get a gun that shoots a great pattern at 40yds. The most important part is the load you use and the choke. You need to match those up and find out which works best. What type of shotgun do you use for your bird hunting now?
The fact is a simple pump or even newer single shot shotgun will work if it is set up right. I have two guns the one I started with - a 28" Benelli Nova and my 21" Mossberg 535 Thumbhole. Both work well. The shorter barrel is a bit easier to swing in the brush.
Now if you are looking for a reason to buy a new expensive gun I guess you have got one. If this is a sport you are going to do for a long time, I recommend a thumbhole stock. Just more comfortable to me. Be safe and good hunting!