When I started riding, I thought that climbing defined "strength", and since I was pretty light (sub 100 lbs), I could climb pretty well when I compared myself to some of my already-racing friends.
However, on my first long ride with more than one or two people, I realized very, very quickly that speed is king. Not sprinting, not climbing, but the ability to go fast for short(er) periods of time (30 seconds to a few minutes). Once you have speed, esp since you looked fit in the thread about bike fit, you'll be relatively fine for everything else. "Relatively" because your sprint will be seriously affected by tactics and genetics and your climbing (longer than 5-6 minute climbs) will likewise be affected by genetics and training.
botto's "racing plan", as often as it's repeated here, is probably the best, most succinct, and most effective way of getting into racing in a somewhat reasonable fashion. Group rides teach you group riding etiquette, some group riding techniques, but mainly gets you used to riding with other people around you while you're going hard.
As far as training goes, I tell people that for the first year of racing, if you train consistently for 3 months, you'll be about as good as you get for racing for that year. Physically and tactically it'll be hard to improve significantly after 3 months of determined riding while in your first year of racing. It's been said that it takes 3 years to get comfortable racing, i.e. you feel "in the groove" immediately at the beginning of the season, not after a few races.
My "generic" training schedule is based on Eddy B's and other mid 80s and early 90s training plans:
Mon: rest or easy spin, like 30-45 min
Tue: sprints, do 10 intervals (start with 3, work up), efforts should be 60 seconds or less. 60 min ride.
Wed: longest ride you can do based on your schedule, ideally 2-3 hours
Thu: pursuit type efforts, 2-5 minutes, only way I can do this is with hills since mentally I can't go for more than 200-300 meters on flat roads. 60 min ride.
Fri: easy spin, 30-45 min. Don't rest, you'll be very slow Saturday if you rest.
Sat, Sun: group ride, 1.5-2.5 hours each.
If Saturday is a big day for you, start the week on Tuesday's workout (so on Monday do sprints), then on Thursday take a day off (you'll need it), go easy Friday, and Saturday you'll be itching to go.
Eat plenty (of good food) before the hard days. I can't go hard if I don't eat a lot.
My thoughts on crits versus road races. Crits emphasize pack riding and/or cornering, along with speed. Road races emphasize crit riding with long hills thrown in. Trying to move up when the field is jammed curb to curb and flying along at 30 mph is difficult enough in a crit, but at least you know there'll be a turn in a few seconds to help break things up. In a road race there are very few turns so people get much more desperate to move up. I've been pulled along in such conditions for miles, can't move up, can't move sideways, guys tumbling into the shoulder on the right, other guys getting DQed for going over the yellow line on the left. Not my idea of fun. Then suddenly everyone slows down because the lead guys hit the hill and then it breaks up a bit. After it breaks up it's all strung out, guys dying to stay on wheels, and that's how the rest of the race is.
Road races are much, much harder than crits, else I'd be entering road races and not crits. For me, a road race is a chance to train on roads where the turns are marshaled for me.
Some of my other thoughts on race specific speed work:
There are more but you get the idea.
hope this helps,