I just traded in my F150 for a 2006 Hummer H3.
It needs an alignment because the tires are wearing pretty unevenly - pretty quick. Before I drop money on an alignment I want to throw some new shocks on the front and back.

Any suggestions? Best bang for my buck?

 

Bilstien remote reservoir 5150 series shocks.

 

All depends on what you want out of your H3. Is it leveled? Do you wheel it? Oversized tires or rims? Shocks are one of the most subjective replacement parts besides rims and tires.

Here is the way I rank them, others may think differently.
Smooth all street ride: Monroe Reflex, OEM, KYB Gas-A-Just, Procomp ES3000, Rancho Rs5000, Bilstien 4600
Smooth ride street and OffRoad: Procomp ES9000s, Rancho RS9000XL
Truck like ride on road and ability to soak up the rocks OffRoad: Bilstien 5100
TOP of the line: 2.0 FOX Racing, ProComp MX6, Bilstien 5160

 

If you're going to be using it off road then you will want to level it. Read up on it, there are lots of threads. Here's a thread on here for doing it yourself.
Torsion Lift

After that, choose your shocks. You'll want them to be a little longer than the OEM. I have the Pro Comp ES9000 and like them.

 

Not necessary, just spacer the upper mount to compensate the lift.

 

I wouldn't bother with Adventure OEM Delco or Bilstein shocks unless/until you mount larger and heavier tires.