Congrats on the new bike! It is beautiful!
In terms of learning how to ride a bike without falling over:
1. I would suggest lowering the saddle a little - have it a little lower than you will eventually want. You will feel safer and be able to easily get a foot on the ground. You won't be going very fast/far on your first rides (or attempted rides) so this shouldn't cause knee strain. Once you are comfortable on the bike, and going out for longer harder efforts, put the saddle back up!!!
2. Look where you want to go - don't look down at the ground, unless it is the road waaaaay ahead of you.
3. It is easier to keep a bike upright if it isn't moving too slowly. Get it going and commit. Try to keep the front wheel steady (do this by following tip 2, and by not looking at the wheel).
In terms of clipless pedals:
This will come, and you will know when it's time. You want to be totally comfortable with the bike first. Soon the bike will start to feel like an extension of you, and in time you will want it to to become even more an extension of you. When that time comes, clipless pedals will probably feel safer to you than platform pedals, especially in "dicey" situations where you need good handling skills and thereby good connection to the bike. You don't want your feet sliding off the pedals when you hit a bump (especially if you are already out of the saddle), or take a tight corner!