Since it hasn't been noted yet I'd thought I'd say--all recumbents are probably more comfortable to ride than an upright bike, but not all are especially more-aerodynamic. The aerodynamics is really where the recumbent advantage lies. Bikes that have lower pedal positioning (such as LWB's and CLWB's) are capitalizing on the comfort advantage of recumbents, and usually don't boast of amazing aerodynamics because they may be not much faster than an upright bike.

For maximum aero advantage, you'd want a short wheel base bike that has a very-reclined rider position. Usually, the higher the pedals are located relative to the seat, the more aero the rider position probably is.You are probably most likely to get this positioning with a highracer, but not too many companies sell inexpensive highracers. Actionbent is one, their supplier has a couple more with not as good specs.

....If you find a cheaper used small-front-wheel SWB, it can often be converted to a highracer by adding on a longer fork and bigger front wheel, but one problem with this is that it may not have any way to attach a headrest. With an upright position you don't need a headrest but on a very-reclined seat, you may. So then you will need to find one that you can attach, or you may need to make one somehow yourself.

*-of course, an awesome athlete can get on anything and pedal it to amazing speeds, but speaking strictly in terms of a bike's naked aerodynamics.
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