If the link in your post is the Weber grill you purchased, you've bought a classic.
There are a couple of methods I've used when lighting charcoal briquets. The first is the stack-squirt-light-run method. You make a 'pyramid' of briquets, squirt starter fluid (in copious amounts) over the briquets, toss in a match and run (if you've used enough fluid the coals will ash over reasonably quick. How do you know if you've used enough fluid? The mushroom cloud that forms is a pretty good indicator).
Less fun and dangerous is the electric starter. There is a device they sell that plugs into a regular electric outlet, which you shove into your pile of briquets. In turn, it gets red hot and starts the briquets, but without fire. This method can add a great deal to your overall cooking time, though. My dad used this method for years, but I learned a fascinating lesson in electricity when he turned the tongs over to me the first time. The electric starter he used was very old and apparently not very well insulated. After plugging it in, I walked back over to the grill in bare feet and inadvertently stepped on the cord. My knee joint still hurts on cold days.
I don't know if they are available in your area but lots of folks are using them here - an ignitable bag of charcoal. You place the bag on the grate, light the bag in several spots and walk away. Apparently there is a starter fluid in the bag's ingredients. I do wonder about the chemicals on the bag from the printing and coloring. I don't believe the chemicals affect the taste of food, but then again I believed for years that when you cook with booze all the alcohol cooked off.
Speaking of booze on a side note, you will want to keep an open can or bottle of mediocre beer handy in case of flare-ups that always seem to happen when cooking fattier foods like hamburgers. Some folks use a spray bottle filled with water for that purpose, but I like to help the economy by using good 'ol American beer to pour on the offending coals (after all you can't really drink the stuff. Although I have heard that the fumes from burning charcoal starter fluid deadens your tastebuds. Truth be told, the fumes from burning charcoal starter fluid can also shorten your nose hairs and trim your eyebrows - don't ask how I know this).
The best method I have found for lighting briquets is by using one of these: http://http://www.virtualweberbullet.com/chimney.html
The one above can ash over up to six pounds of briquets, which is enough to cook a small cow to well done.
They're usually between $12-20 us, or you could try making one as shown here: http://http://www.opentutorial.com/Make_a_charcoal_chimney
As for clean-up, that's easy. Leave the grate in place after cooking and allow the remnants to burn over the extinguishing coals, then just before the coals go out, go to town with a grill brush and the remaining mediocre beer (you didn't drink it, right?) Allow the coals to go to complete ash and cool down (this can take between 24hrs and 6 weeks depending on the amount of coals you've used when cooking) before dumping them into the trash bin.
Enjoy your new grill!
RE