There is no "depth" necessary to be aero. Shimano's 24mm deep times actually test pretty well, on par with even some wheels deeper than 30mm. I don't know what kind of budget you are thinking but I've heard great reviews of Hed's 23mm wide rims and they are actually as aero as many wheels deeper with a 23mm tire. Tire choice can affect aerodynamics as much as wheel choice. Typically a wheel that is 19mm wide at the brake track is significantly less aero with a 23mm tire than a wheel that is 23mm wide at the brake track of the same depth.

All that aside, I would go for a set of Hed's C2 aluminum wheels. A little more aero, the wide rim bed has been reported to be more comfortable, corner better and they get overall good reviews.