The small block Chevy is a great little power plant. There are so many things that you can do, some more expensive than others, but you've got to know what you have.
1. Do you know the year of the engine?
2. Look at the ends of your heads and tell us what shape you see embossed;
• Check this page to help you identify them;
http://www.fastnuf.com/Headguide.html
3. Do you have a two or four barrel carb currently?
Air flow through the engine is key to performance. The later the engine, the more restrictive the flow. Hopefully your 350 is '72 or earlier but you can work with later models. The heads and compression will determine how much performance you can squeeze out without machine work or replacement.
Dual exhaust will probably be the most dramatic (noticeable) change you can make on your stock engine. Some may be psychological from the sound, but you will see and feel a real difference. A nice set of headers will improve that too but be careful, a cheap set will leak, sound tinny and won't last.
If your heads are earlier (camel humps are awesome!) they will flow nicely as is, with the exhaust and add a nice, torquey intake manifold with a small, spread bore carb. You could be very happy with the results!