I'm more into cycling for fun (allowing the benefits of the exercise to be somewhat accidental) rather than short, intense rides aimed specifically at calorie burning like you seem interested in. Hopefully somebody more into your specific goals will give a better answer than I can. You might also have good luck asking more specific cycling questions on Bicycles.SE.
One comment: 30 minutes is a very short ride by cycling standards, so my answer tries to focus on a short intense ride.
There's on-road cycling and off-road cycling (and lots of variations in both). You can burn calories and breath heavy by pedaling hard and fast in just about any kind of cycling on any kind of bike.
Most people that are interested in burning calories fairly fast would go for a road bike (lightweight, drop handlebars). Off-road cycling is more likely to have more "technical" bits where you're worrying more about maneuvering than speed or power and often harder to find good places to do it. A road bike will tend to be more fun when you're pushing hard just because you'll go faster and find the handling of the bike works better when going fast like that. There's various sub-types of road bike, and again, you can get a decent workout on any bike. The road-bike geometry with a relatively vertical seat tube that places your center of gravity over the pedals and gives you plenty of handlebar leverage to pull down is probably best for maximizing how much effort you can put out.
Make sure the bike fits you well. Maybe even pay a bike shop extra to do a precise fitting. Be prepared to go through a seat or two before you find one that works well for you.
You can either keep a moderate cadence against moderate resistance, or a high cadence against light resistance. If you plan to go with a high cadence you may find that the best solution is special "clipless" pedals and special shoes with cleats that click into the pedals. If you go that route, make sure you have a really good fit (or pedals that give you a bit more "float"), since a poor setup with your feet locked to the pedals can cause knee problems. If you're not sure you could try more traditional toe clips and straps.
For relatively short rides like you seem interested in, one bottle cage and one water bottle should be fine. If you work your way up to rides over an hour or two you may want to get a second bottle cage and bottle.
Some people find it easier to maximize things if they have some numbers to track. Basic cyclometers just have a wheel sensor (to give you speed, distance, time, max speed, avg speed, etc), but you can also get ones with a crank (pedal) sensor to tell you cadence (how fast you pedal), and some can also connect with a heart monitor which will give you the best idea how many calories you're burning. I use a basic cyclometer, but I believe if you go with the ANT+ wireless type setup you could have that heart rate sensor working with an on-bike cyclometer display or an on-wrist watch type display (useful for non-bike exercises).
You can warm up and cool down on the bike, just take it a little easier at the start end end of the ride. Plan your routes so that the hardest parts are in the middle.
As far as specific exercises:
- Get on the bike and ride -- any kind of riding will burn some calories, make you breath harder and make you sweat. Clear your mind and pay attention to cycling.
- Pick a route and try to do it as fast as possible.
- Pick a round-trip route and try to get as far in 15 minutes as you can (then turn around and keep the same speed on the way back).
- Sprints -- try to go really fast for a brief while. Maybe try to ride with friends and race each other to a town limit sign or something like that.
- Hill climbing -- climbing is good cardio. If you go too slow up a hill the bike is hard to control, so there's some extra motivation to push yourself hard up the hill. I always find my heart pounding hard at the top of a good-sized hill. The steeper and taller the hill the more work it is to get up. Don't be afraid to use your lowest gear, as long as you keep spinning the cranks, and you might have to get off and walk the bike up some hills when you're starting out. If the climb feels easy, do it faster.
- Intervals -- push yourself really hard for 30 seconds, ride easier for a few minutes then another push. (rolling hills or repeated sprints are good ways to get this) I believe runners do similar interval training.
- Bike to work -- I assume your 30 minutes is because of time limitations, if you ride your bike to and from work so that your commute becomes exercise you can turn what used to be sitting-in-a-car time into exercise-on-a-bike time and increase your total exercise time. Bring a change of clothes and use a couple moist towelettes to clean yourself up quickly in a restroom stall when you get to work, and save the more intense workout for the ride home where it's okay to show up super-sweaty. I get 6-7 hours of cycling in a week just getting to and from work.
Most areas have cycling clubs where you can do social riding with other people, but those are usually for multi-hour rides, not 30-minute rides. Finding a group you can go on a long weekend ride with now and then would be good, especially if they're the more competitive sorts that will help push you to work harder with races to signs and things like that. Races to signs with friends will get you intervals without thinking about the exercise part. From what I've seen, these kinds of cycling clubs usually post the intended pace (or friendliness vs competitiveness) and terrain for all the planned rides.
General results you see from cycling are mostly what you'd get from any kind of cardio. You'll likely get more leg strength and muscle definition, especially in your quads; moreso if you push hard now and then. If you keep good form (flat back, weight off hands) you'll get a light amount of static core exercise, especially along your back (sorta like a plank).
- Fry Fat With Intervals
An article on intervals that includes some estimates of calories burned depending on cycling speed.
- Velominati - The Rules
Some (humorous) inspirational rules to help you learn to be a hardcore fast cyclist.