I have a 5.3 in my truck. And I am in a similar boat...
Does it have exhaust at all? Is it lifted have big tires or what? What kind of driving do you do on/off road? How much do you want to spend?
Put a full exhaust on it, headers/cat, muffler. Put an intake on it. Get a custom dyno tune, i took my truck to a shop called Pro Dyno, ask for Charles he's a great guy and knows his stuff.
You could also do a cam and stall converter. Depending on the questions above I could reccommend a cam from what I have been told and researched.
You could also do forced induction either a turbo or blower, also based on the questions above.
Also as mentioned above, new heads and a ported throttle body.
The stock drivetrain could handle exhaust, intake, tune; when you get a cam you might need to upgrade depending on the cam. And if you get the FI you would definately need to upgrade the transmission. I know a lot of guys use finish line transmissions, or if you know someone local that could do it (pro dyno probably does).
I have done the cam heads headers etc NOTHING compairs to a Magnacharger the best dam $3800 I have ever spent. Best of all you can pull it off when you sell and put it on your next ride mine has been on 3 trucks Has over 300000 miles just change the oil.