I can confirm the 1406 has an electric choke and is 600 cfm; that's what I purchased for my LS4 swap. The carb is configured for the LS family out of the box, so my initial gut instinct is that it is too much carb for that 350 you have, as that is a much more mild engine.

I would definitely recommend getting some tools for tuning your carb. At an absolute minimum, a vacuum gauge. A bit nicer would be a manometer, and really nice would be a wideband O2.