1. Long, hard, distance rides: Criteriums are often considered harder than road races because of the repeated tight cornering, and the limited opportunity to recover between accelerations. BUT, don't think that road races are easy. Beginner road races (Cat. 5) are typically only 15 to 30 miles long, so they can be pretty fast. And although you don't have the constant accelerations that you do in a crit, you still have pace changes that come from turns, hills, gaps, breakaways, surges, etc. You might be able to cruise at 24 mph all day long, but if you can't accelerate to 28 to 30 mph for a while, then recover at 24 mph, then do the same thing 20 or 30 times during the race, you're going to end up getting shelled off the back. And once you've lost the draft, you're toast.
The most effective training to prepare you for speed changes is intervals.
2. Finding local races: Check with a couple of LBSs in your area to see what the riding "scene" is. Join a local club. Tag along with a local team on their training rides if they don't mind. Get a feel for the pace changes that typify group rides. Learn to feel comfortable riding in very close quarters with other riders. 50% of racing is fitness (i.e. interval training) and 50% is drafting (i.e. bike handling skills).
3. New Bike: Honestly, I've seen guys with old steel 10-speeds with downtube shifters kick a$$ on guys with $6000 Colnagos. It truly is not about the bike. It's about the engine. I'm not telling you to never upgrade, I'm just telling you that on your list of priorities I would work on fitness first, bike handling/group riding skills second, and then think about upgrading.
Bob