Depending on your budget you won't go wrong choosing either Canon or Nikon DSLRs.
A good entry lens to bird photography is 400 mm.
My suggestion would be a combo of ...
1. Canon EOS-7D, EF400/5.6L or
2. Nikon D300s, AF-S 300/4D ED + TC14E II
Both rig would be very portable.
Getting the DSLR camera and lens is one thing. Don't forget there is another major undertaking in digital photography which is Post-processing of your image files!
A learning curve that you need to invest time in it.