I Want to Ride My Bike Faster Than Everyone Else.

You say you ride to school. Does your school have a cycling team? Collegiate cycling is an awesome, awesome way to get into racing, especially for women.

I'm in generally good-great shape (in addition to cycling I run a lot and dance A LOT), but wouldn't describe myself as "athletic" (i.e. I'm pretty darn fit, but not actually any good at sports) Stop. First up your fitness level. Become the athlete, then worry about the gear. It ain't the shoes, its the fitness that will turn you into the athlete.

Your bike is fine to try and pedal into the ground, and I did many many miles in your position on SPDs (though I've never raced yet). Karathrace is right, just start putting miles on your body, over as long of stretches of unbroken pedaling as possible. One way of doing this is to make one leg of your commute a longer ride with extra out-of-the-way miles. If you start getting chafed or too sweaty and heavy, or other clothes/skin-related annoyances, that's when spandex starts coming into play. Climbing is the real cycling challenge with me, but there are winning climbers (Nibali), sprinters (Cavendish), and all-arounders (Cancellara), so it really depends on what you want out of riding and what your genetics and fitness level allow you to be good at. Fast will come by itself. You won't have to worry about riding in groups for a while yet, but many riders out on the road are amenable to trading off taking the lead and learning how to draft a little bit. It's a little presumptuously dangerous to get all 4" away from a stranger's rear wheel because you're trying to practice riding in a ProTour peleton. Frankly, from what I know about Cat4/5 races, the greater skill is being able to stay away from people who would crash you out while still getting ahead.

Oh, and I notice you are a grad student. That's totally fine. I would estimate over half of collegiate cyclists are grad or professional students. It is not an NCAA sport, so all you have to be is a full-time student.

Club rides for sure. Best place to learn to ride in a group. Start at the bottom and work your way up. The downside is that you probably won't be the only learner there, but there should be plenty of experienced folks to help you out. If it's anything like mine, you'll have crit racers at the top-graded rides. If your location is correct, http://www.tbn.ca/ looks like a good place to start. SPD pedals are fine until you're averaging 18-20 mph over 50 mi (sorry for the imperial units). You should get a real cycling computer though.

Okay, I just looked at the ride classifications. You probably don't need to start at the very bottom, but don't push it. It's way easy to get burnt out killing yourself on one ride, or to get discouraged when you realize you're holding the group back. And by "you" I of course mean "me".

Hey! I'm a female amateur bike racer (road, mtb, and cyclocross). I agree with the above commenters - you seem to be just fine with the equipment you have (although watching the ProTour will definitely have you thinking otherwise:)). One thing, though - If the jerseys you own are pro team jerseys, you'll likely have to buy a plain one. I've gone to races where they strictly enforce this rule - you can't advertise for a sponsor if you're not part of that team. It's okay if it has a brand name on it (like Pearl Izumi or Castelli or whatever), just not a replica jersey. I have raced road on SPDs for years - they are just fine as long as you're comfortable with them. Dual-sided entry is actually something I prefer - you'd be surprised how many folks struggle just to get clipped in when the gun goes off. Meanwhile, you're 5 pedal strokes ahead of them and can grab a better position. As far as training plans, I'd recommend Joe Friel's book called The Cyclist's Training Bible. It'll introduce you to the concept of periodization, and even provides instruction on how to create an annual training plan so that your fitness peaks for your target race(s) of the season. Some of it is hinged on having a power meter, but you can get by just fine without one (using heart rate or rate of perceived exertion instead). I bet you can use your commute for many of the targeted workouts he has in there. There are so few women cyclists out there compared to men, so it's super easy to go out and make friends. Once you start racing and get into the community & group rides, you'll realize how many resources open up to you - Use them. Ask questions. Most importantly: HAVE FUN! Racing is a blast.

Work on your weaknesses. General fitness and endurance is good, but in a race the peloton will split, and if you're not in the lead group you want to be able to bridge that gap. That can mean an extended burst of all out speed to catch the lead group, followed by tempo riding, and then you need to be able to contest the sprint at the end (if you're in it to win it). That's hard to do. So keep riding, keep training, and incorporate hill and sprint repeats into your workouts. As far as the gear goes, upgrade those pedals. They're totally fine for commuting, but I wouldn't feel comfortable cornering while pedaling with them. If you're going to race any crits (crits are the most fun!), you're going to want pedals that allow you to corner fast and keep pedaling.

Once a guy was in our race fully decked out in a http://en.wikipedia.org/wiki/Rock_Racing kit. The race official berated him at the start but let him race anyway, so yeah, take TessaGal's advice about not wearing team jerseys.