It is really a lot better to ride with padding. I mountain bike and wear Pearl Izumi spandex. Before leaving the house I just pull on a regular pair of shorts over them that I take off at the trailhead. Then, after riding, I change out of the shorts into regular clothes (usually as quickly as possible in the car with a coat or shirt over me), since we usually go out to eat after riding. You shouldn't wear the padded shorts for too long after riding, since most people sweat when they ride.

As far as the shorts being tight, they shouldn't be pinching you uncomfortably while wearing them, they come in lots of sizes... And remember you don't need to wear underwear with padded bike shorts. But personally I wouldn't go off the trail with just the spandex on, either. While out riding, I don't really care.

Also, the front of your bike seat shouldn't dig into any of your areas down there... make sure the front isn't pointed up too much. You may need to move the seat a couple of times until it feels right for you.