Perhaps the '80s beach-girl term "let's do it!" will suffice. Not so clinical as "let's have sex," lacking the animal overtones of "let's fuck," certainly rougher than "let's make love." If you want some intensity, but without the leather gear and ass-slapping, "let's do it" may be your phrase. It implies fun and a deal of reckless abandon without going totally wild and concentrating on the physical--it's a way of saying "I think you're sexy and I want your body" without the being overly euphemistic, yet without being totally raw about it.