How do you stop the bike? In the saddle? Maybe if you practice standing briefly as you pedal, the starting and stopping out of the saddle will feel more natural. Remember, the bike will be more stable the more weight you put on the pedals rather than on the saddle. Try putting one foot on the pedal as you straddle the bike and pushing on the ground with the other foot like you're riding a scooter. That's the starting motion.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72