I Want To Beef Up My 340 Motor (help Please)

If you want more performance the 4 most important things you need are:

A. More Cam.
B. More (deeper) gear.
C. Freer flowing exhaust.
D. Stall convertor on an automatic.

Exhaust that flows well is as critical as a higher rate cam and gears are the most critical part, choose the wrong ones and performance suffers, likewise with a torque convertor.

I know that 3.23 gears won't work too well with much of a cam, especially with an automatic and a stock stall convertor.

In all honesty, deciding HOW fast you want to go and choosing a balanced package (Cam, convertor, exhaust and gears) for your purpose is always best.
All that being said, don't use too big of a carb, a 700 vacuum secondary carb is as big as a street-run 340 will need.
Avoid Holley Double-Pumpers, as all the tuning in the world, on a small cube engine, will not make them work correctly.

Mark.