Helmet mounted mirrors work for some, but not for others. The vision in my left eye is minimal, so I prefer a bar mounted mirror (as mentioned below).

You didn't say what type of riding you plan to do.

Regardless of type:

Mountain Mirrycle mirror
Ergonomic grips and (possibly integrated) bar ends. (whatever you find comfortable)
Water bottle cages
Water bottles

*Multi-tool
*Spare tube(s)
*Inflation device (either a pump or CO2, or if paranoid like me, both)
Something to carry the above.

If wet weather riding is in planned, fenders would be essential.

I personally would add a rear rack, a trunk bag and lights... I always use my rack with a trunk bag, and sometimes panniers for all-day trips. I have only used my lights a couple of times, but they are always good to have just in case.