The chipping should usually be done first (try to think about how the vehicle would naturally accumulate damage/dirt/dust/fading) depending on the type of chipping you want to portray. I personally don't go in for the chipping approach as a matter of taste.
My own approach to weathering follows these steps:
1) Base coat and camo colors applied by airbrush
2) Airbrush mist coat of base color (for camo jobs) to tie colors together
3) Seal base coat (I work in enamels) with Future, apply decals, seal decals with 2nd coat of Future
4) Apply an overall wash (usually Raw Umber)
5) Apply dot filters
6) Apply pin wash (usually Burnt Umber)
7) Seal everything with lacquer-based Testors Lusterless Flat
8) Apply pigment weathering where desired
If you check out the build logs I have on my website, www.bpmodels.net , you'll see some step-by-step photos and descriptions of how I achieve my results. Others will do things differently with different sequences or materials depending on preferences so there's no "one true way" when it comes to weathering. Try out what works for you and fine-tune along the way and develop your own style over time is the best approach IMHO.
As for the brush to use with dot filtering, I usually apply the dots with small brushes and then blend the dots together to create the filtering effect using a square tipped blender brush (different sizes depending on the size/dimension of the surface I'm working with).
HTH!