I try to avoid 3 lane roads and roads with no shoulders except at really low traffic times (i.e. early am, weekends), so Taren Point Rd would get crossed off my list.
This route from
http://www.bikely.com/maps/bike-path/Ca ... -to-Sydney might give you some good ideas. It's not using the Bay-to-Bay cycleway along the beach between Dolls Pt and Kyeemagh, but the roads it chooses are pretty tame. A tamer option would be to ride up to Clareville Ave, north to Sanoni Ave, east towards the bay, and pick-up the shared pathway just west of the Sailing Club. Then head north to Kyeemagh, and decide whether you want to take a short-cut up Bestic St (it's usually tame enough).
The bay-to-bay pathway south of the Sailing Club is very narrow - and usually get walkers with dogs etc.,. bringing you to a stop.
To get your confidence up and bike sorted, try doing some runs out to Kurnell, using the cycleway from Taren Point to Kurnell. If you stop at the coffee shop at Kurnell (in a.m.) there's sure to be a ton of riders who you could ask about group ride etc.,. Also try the run to your work on a weekend or evening so you can get an idea of what it will take.
Last suggestion: get a good mirror - like the
mirrcycle. It's a lot easier making lane-changes and turns if you can watch for breaks in a rear vision mirror. Can't recall if Frasers Cycles (on Taren Point Rd) stock them, but Clarence St Cyclery and a number of others do.
Cheers