Here is the general scoop. There are a ton of different recumbent designs. A bike with a relatively upright seat will climb OK because you will have a closed hip angle. But it won't be as fast on the flats or downhills as a typical aero bike. Some recumbents will actually be slower on average than a road bike, but the majority will be faster.
If you get an aero bike like the Bacchetta Carbon Aero II, you will be about 15-30% faster on flats . (This is assuming that you are riding at 18+ MPH. I am in good shape, but not great shape, and have yet to be passed on the 70 mile loop I do around here. It's also has some Cat A bikers. However, they do blow by me on the hills. (I have a Titanium Aero.)
There are faster all around bikes than the one I ride that do climb better. The French front wheel drive carbon low racers with moving bottom brackets will likely climb as well as any road bike and will be faster than my Aero on the flats. That's a two-for-one, so lone as you don't get run over by an SUV because your butt is 3" from the ground. I generally prefer my high racer for safety.
For details on the physics of recumbents, see:
http://web.archive.org/web/200801120...ish/espeed.htm
You do need time to strengthen your recumbent muscles. But you will probably make the journey to work in significantly less time, rather than more, after a month or so. I've shaved about 10" off my time, which allows me to open up my route more!
Finally, bentrideronline is the place to go to poke around for people's opinions about their favorite bikes. Here is an example of a low and a mid racer:
http://www.velokraft.com/ M5 makes a wide range of bikes as well.