I have a '86 350 TPI (from a long block crate motor) and I use the stock
ECM and chip. It's plenty good enough for engines below 400HP. As long
as all the original TPI stuff is in place (plenum, runners, manifold,
TB, sensors, Cold start injector, et) and are stock or OEM stock
replacement; that's the way to go. My ECM and chip are for an automatic
transmission which I replaced /w a T-5 Manual years ago. That shows the
relative flexibility of this system. You don't say whether you own a TPI
or 4-bble carb. But I imagine that if this works well with the TPI, the
4-bble carb ought to be a snap. After all, everything below the intake
and fuel systems is common stuff. Heads, pistons, valves, et. are pretty
much the same. So keeping everything stock is a good place to start,
then you can go on from there. The Stock ECM should provide every thing you need. Chips are available from: JET and Superchip, among others.

Mike Richardson answers: 

here is the big problem with increasing cubes 305 tpis came with 19lb injectors with a Prom (chip) calibrated for that flow rating
if you install a 350 your going to want to run the 305 injectors with 305 chip you cannot swap these around because you will have horrible driveability 350 injectors are rated at 22 lb and must be used with a chip set up for a 350 if you try to run 24 lb injectors with the 350 chip you will run so rich that it will kill power unless you get a custom chip burnt for the bigger injectors. Since you had a 305, if you have any mods done to the 350 like cam, heads etc you are going to want to step up to the stock 350 set up bare minimum injectors are very pricey and superchips will work fine for a chip unless you want to pay double for a stock piece