Once you get over the initial heebee-geebees, I'd recommend going clipless. Since the feet are part of the steering, having the feet connected directly helps to make handling the bike more consistent and predictable. If your feet aren't connected, they can shift or slip off, and any such changes can negatively impact how the bike handles. The nuances of riding clipless will come with practice and miles.
For intersections, I stay seated and laid back most of the time, putting my dominant foot down to stop. The trick is being in the best gear for starting before coming to a stop. If I see a yellow or red light ahead, I shift from my 52t chainring to my 36t, and from whatever cog I'm in, up to the second largest 27t on my 11-30 cassette. I get to the 27 by shifting all the way up the 30, and then back down one. It sounds like a lot to do, but after a while the fingers just do it quickly by themselves. If it's a slight uphill, I'll stay in the 30; if it's a slight downhill, I might drop down two, to the 24 and let the hill help. For surprise or fast stops, where I'm in the wrong gear...that's when I break out the Fred Flintstone push and the butt slide. That doesn't happen too often though.
The best gear for starting will vary from rider to rider. Try laid back starts on flat roads in the easiest cog/gear first, then work your way down the cogs at successive starts until you find the cog that is just a little too hard to start easily. One cog up from that should be your best starting gear.