How slim a budget? First thing is inflate your tires to the proper air pressure ;-). You can do a lot with the 6.0L PSD but really just depends on what your level of mechanical skill is and how much you want to spend. One of the lowest cost upgrades is an air filter, BUT if your going into the dirt I would NOT recommend the super high flowing reusable filters. I have always suspected them to not have a fine a filtration capacity as stock style (at the cost of air flow). The next might be a Tuner. I think you have a lot of choice, they are all around 400 bucks and often have many levels of tune ability. Some do 'suggest' other modification to your exhaust and other parts so check carefully and don't expect the crazy claims, but do expect a good seat of the pants feel with them. Turbo updates, exhaust system, intake system, etc all do well on the PSD. One thing if you do go more then Stage I power is the mandatory Exhaust Temp Gauge (EGT).
I agree with TheRipper. The most bang for the buck will be high-flow exhaust, ECU tuner and probably cold-air intakes. Companies like Banks and Bully Dog probably have packages that will take the guess-work out of mixing and matching the right parts.