I just bought a 2002 F250 7.3L with 200K miles and I would like to improve the towing capability and maybe the fuel economy when not towing something. I am looking for good ideas of things to do or stay away from. The truck is a stock (from what I can tell) 4x4 with an automatic. I am not looking for some crazy tune that will give me lots of power but melt down the engine or blow up the transmission.

 

A great place to start is a TS 6-Position Chip, it gives the truck a little more pep in it's step. If you do ANYTHING make sure you get a gauge pillar that shows EGTs, and Transmission Temp. Upgrade your aitfileter to the NAPA mod or similar. You could also do a wicked wheel II, that'll help with everything.
But before you start down this long road, make sure your truck is at 100% otherwise repairs will get expensive quick.

 

Another option is the PHP hydra chip, there are a ton of threads on here that you can read till you go cross eyed on the pros and cons to both.

As mentioned, getting the truck to 100% before adding any power is a big one. There are a lot of things to look at, as mentioned simple air in (6637, AIS or S&B intakes, again lots of info on these) and air out (4" exhaust) make a difference in these rigs. Then there is checking your CAC system for boost leaks, checking the up pipes for leaks (replace with the bellowed ones if they are leaking, Dorman or IH are the most popular options on these), hutch and harpoon mod, etc. if you look in the tech folder sticky you will see a whole host of preventative maintenance items in there.

Welcome to the forum, there really is a great group of guys here willing to go above and beyond to help. You found the right place!

 

6637 filter is probably your cheapest bang for your buck. Ditch the stock filter and don't look at it again. The stock filter and housing really doesn't flow well at all. I tested mine years back by removing my dirty 6637 and reinstalled the factory filter(brand new filter) and the difference in power was drastic. You could get a more expensive filter and housing, but $40-50 for the 6637 has worked pretty darn good. I'm used to loud vehicles and the turbo noise has never bothered me. Kind of soothing actually.