Golly, I just love open ended questions like this one!
There have been a number of articles about budget build-ups for the stock 350 Chevy motor. Power is made in the heads IMO, and IF you can swing better heads then the stock units, by all means buy some. If you can't, change out the stock cast pistons for some higher compression hypers or forged pistons. If you are stuck with the stock heads, keeping the compression reasonable at 9:5 or less helps--at least make it better then the soggy 8:1 you most likely have now.
Go with a good, mild performance cam that won't overshoot your stock heads. I went with a Summit K-1103 cam for my motor, but may change it out since I have aquired some Edelbrock RPM heads in the meantime. A mild cam that has about 214/224 (degrees of lift) @ .050" and .488 lift will work quite well with the stock heads, and even better with performance heads (I hope I said all that correctly--I'm nursing a brew). A performance aluminum intake is a must IMO and so is a decent carb. Both are fairly reasonable and are available as a combo from places like Summit Racing. With the above parts and stock heads, you can easily make 300 genuine horsepower. That will move a Z and get reasonable gas mileage unless your foot goes down on a Holley DP (I'm not building my Z for mileage if you know what I mean).
If you can swing a performance distributor and ignition, you'll pay yourself dividends in the mileage and performance arena. Some block huggers won't hurt either, but how much $$$ you want to spend makes a difference. I buy a lot from ebay and have been very pleased with the results. Also, Nothern Autoparts is a great place to buy from as well.
Hopefully this gives you some ideas.
Davy