I'm new to cycling too and am about to buy my first road bike when I get my bonus.

I too am afraid of riding alone but realize that my fears are probably unfounded. I always try to ride on the bike paths in the middle of the day when it's light outside. I carry a fully charged cell phone which actually is trackable via "find your iPhone". The bike path close to me is quite deserted and goes through some shady neighborhoods going south and runs along the parkway going north. As I ride more, I've become more comfortable with riding alone though I do look forward to the day that I can participate in group rides.

As far as equipment, I started off with a helmet and my regular sneakers.
As I've gotten more and more into it, I've also purchased some breathable T-shirts, cycling pants and shorts(Can't ride in my yoga pants because they keep getting caught in the chain) and a wind proof jacket. My bike came with a water bottle cage but I carry a spare water bottle (along with a cell phone, tissues, and money) in a small backpack.

Good Luck and Happy Cycling.