I guess the first question is: How long was this class? And a corollary: How much longer were pedaling than the longest you’ve gone previously? Because my belief is that the pain has something to do with the bike, the bike setup, or the fact you haven’t spent all that much time on the bike.
And this last point is something you’re going to have to keep in mind as you begin real training. The simple fact is that road bikes are an ergonomic nightmare. You’re sitting on a hard, narrow seat, bent over, spinning your legs in a way that is not duplicated elsewhere in life. So if you go from occasional mountain bike rides to something like 40-mile training rides 聴- all of a sudden -聴 pains are going to emerge. It could be that the saddle height is wrong (my guess, too low) and forcing your calves into an uncomfortable position, causing the cramping. Of course, that could also be due to some chemical deficiencies, particularly potassium. My calves cramp on occasion, usually when trying to crank hard up a hill and I put too much foot action into the pedaling motion in an effort to gain a little speed. Anyway, first thing to do is take the road bike to a shop and check its fit. Even if the frame is the wrong size, there are lots of things that can be done to make it more comfortable.
The aching feet sound like a shoe problem, although again bike fit could be the culprit. If you’re saddle is too low, your legs are going to bow out, torqueing your feet in such a way that the outer side of one foot, if not both, could start to hurt. But I’ve had foot pain in Sidi shoes myself. They’re basically unpadded shoes with minimal arch support. What I’ve found helpful is to insert a pair of Spenco Arch Cushions ($15), which provide cushioned support from your heel to just behind the ball of your foot. So they don’t take up much space, yet provide lots of cushioning and support where it’s needed.
Otherwise, the answer is to find some shoes that fit better. Go to an outdoor or bike store that carries a good selection, find a salesperson who knows footwear, explain your problem, and starting trying on shoes.