What I used to do when I was studying all of the networking terms and different connections was to lookthings up at www.whatis.com . Once you sort through all the advertising, it's chock-full of useful info. :)
I can give you a quick run-down though, of the ones you mentioned.
T1: 24 64Kbps channels. Used to be copper, now it's mostly fibre that's being rate-limited to 1.544 Mbps. Euro equivalent is an E1, which I think is at 2.05Mbps (30 or 32 channels, IIRC).
Pros: Dedicated, and (mostly) reliable. Known technology. "Enterprise-class". For real businesses that need a real connection.
Cons: Costs a lot to have that reliability. Will charge you a connection fee, equipment fee, a monthly "normal" fee, and a "usage" fee (usually $x per GB).
DSL: Digital Subscriber line. For Home/Small Businesses that don't need the reliability of an enterprise line. Comes in a variety of flavours:
ADSL (most common) is "Asynchronous DSL", meaning your "downpipe" will be much larger than your "uppipe" (to use my wife's terminology :). Meaning your downloads will be something along the lines of 4x faster than your uploads. Not typically good for serving up websites.
SDSL: (Next most common -- used by business/SOHO): "Symmetrical DSL". AS you can guess, your upstream is the same as your downstream. A bit more "businessy".
Search around for more types.
Pros: Relatively cheaper, and you can get "Server" versions of them where you're permitted to host your own servers (WWW,FTP,Mail, etc). Usually have to sign a contract for "business" versions. Setup costs are relatively cheap, monthly rates are low, and usage is either not charged for or damned cheap (relative to the cost per GB on a T1). Typically comes in 1.5Mbps, 3Mbps, 5 Mbps and 8 Mbps packages.
Cons: You need to be close to a CO (Central Office). I believe after about 1km, your signal degrades by up to as much as 15%. (someone correct me if this is wrong). You're better served if you're right next to a CO, but chances aren't that high that you are. :) Tech support can be a nightmare. You're not much better than "Joe Bloe", even though your money is riding on this site being up. Too bad, so sad, you didn't pay the money for a real connection. :)
Bonding typically means to bond one or more physical networks into one logical connection. So, in theory, you could take your cable provider's connection and your ADSL provider's connection and bond them into one logical connection. Doesn't work very well in that scenario, but works well when you actually have several physical connections from the same provider (eg: 2 T1s from Sprint, etc), and works very well with multiple modems. I believe that is a common usage. 2 modems, 2 phone lines, 1 "connection".
Burstable: Means that although the stated "limit" of your connection is say a T1, at 1.544Mbps, it's actually capable of "bursting" for short periods to a higher level. This is because the modern-day cable they bring into your office is not JUST a copper T1, but usually a fibre cable and switch, but is rate-limited to 1.544Mbps.
Pros: If you're saturating the link to do backups, etc, it's handy to speed things up.
Cons: This is completely up to the ISP to provide, and they can charge you money for this option AND USAGE while bursting. sometimes only available if the upstream switch/router isn't already saturated with other customers' data.
Whew. I hope that answers some of your questions. :)