I always wear a sport tank top under my jerseys - I am tall and that way when the jersey rides up a bit I am still covered. If you do not wear anything under your jersey make sure you put sunscreen (yes, I am hopeful that we will need it!!) along your back between your shorts and jersey - lots of ppl have gotten bad burns there from leaning forward.
I also have sleeves that I wear in the mornings and then are able to take off and put in the pockets on my jersey. Got mine at MEC for $20 but you could take any old long sleeve shirt and cut the sleeves off - tuck the top of the sleeve under the bottom of the sleeve on the jersey.
To answer your questions as best I can. Most professional cyclists and experienced amatures wear what is called a base layer under their jersey. This can be a t shirt or tank top but (an this is the important part) it has to be made of a wicking material not cotton. This will help to keep your skin dry and your core temp regulated. If you watch the Tour de France, even on the hottest days up the highest mountains when the riders un zip their jerseys you will see the tank top underneath.
The easiest thing to do is to go to runners world and get such a light t shirt or tank top, or to a cycling store and buy a base layer. I have a bunch of Nike "Dry Fit" shirts that I use.
With respect to what to do first thing in the morning the old marathoning trick is to wear sweat pants and or sweat shirts and long sleaved tee shirts that you dont wear anymore (maybe they were a corporate give away) and simply through them in the garbage when you start riding and have warmed up.
Lastly arm warmers are very useful part of your bike kit. These are lycra sleeves that you pull up and the top tucks under the sleeve of your shirt (they make leg warmers too). They are great for keeping your arms warm in cool morning air or if it starts to rain. When you warm up you either just slide them down around your wrist or pull them off and stuff them into your back pockets as they are so small. If you do decide to buy a pair they come in various weights (fleecy warmer ones or simply lycra coverings). I assume we will not be needing hte fleecy ones.
I just picked up some feet water proof socks for tomorrow. Plus a biking rain jacket. So yes i to have spent a few dollars to make sure my ride is comfy. If the humidity is what they say. All we will need is our shorts and a Jersey on. At that point let it rain to cool us off.