This is probably the best start for information regarding using a small offset -- which is what your Char Griller is.
http://www.homebbq.com/library/SmokerModifications.pdf
Except for what Dan says about thermometers, it's all pretty much gospel.
Just to keep terms straight, I think of the two boxes as the cook chamber and the firebox.
Of the two grates that go in the firebox, the lower one is a charcoal grate, and the other is a food grate -- in case you want to use the firebox as a small, direct grill. You NEED the lower one pretty much where it is, although it will work better if you get it to sit a little higher by making legs for it with bolts, nuts and fender washers. Airspace is a good thing. As to the upper grate, turn it and fit it in to protect the door vent, the way Dan has did it on page 4. That's the first and most important modification.
If you've got company coming this weekend, don't panic and run around like crazy to get the baffle in and the flue extended. Those changes are very helpful, and you'll be glad you did them, but ... no need to make yourself nuts. You can have a very successful cook before you make them. The same with the charcoal basket. You definitely want one. Your life will be simpler (and less expensive), but no hurry.
On your original question -- generally it's not a good idea for beginners to work a straight wood fire in a small offset. It takes a lot of tending, and lots can go wrong. I think most users would agree that your best heat source is a good, hardwood lump charcoal. Although -- if there's a Home Depot around you might want to pick up a few bags of Rancher briquette. Everyone seems to think it's as good as almost any lump, plus it's cheap as can be.
Whatever you buy, for your intended cook, you're probably looking at about 20# of charcoal (without a basket), so make sure you have about twice that much on hand.
Prep your firebox the way Dan shows on page 4, then fill it a couple of inches below the top door with unlit charcoal. Mix in three or four hardwood chunks. Hickory, apple, maple, pecan, peach, oak are all good choices, but mesquite isn't particularly good with pork. Fill a chimney starter with charcoal, get it going well (about 15 minutes, usually), so flames are shooting out of the top, and dump the lit charcoal more or less evenly on the top of the unlit charcoal/chunk.
Open the chimney vent all the way. Open the door vent all the way. And walk away for fifteen minutes. Come back and check to make sure the fire is going well, and close the door vent to about 1/2 way. In another ten mnutes the fire and temperatures will more or less stabilize and it's time to make the last vent adjustment before putting the meat in. If you have an oven thermometer or digital probe or better yet a dual-probe, wireless, remote read like a Maverick ET-73, take the temperature and adjust the vent using 225 - 235 F as your ideal, target temperature, and 1/4 open as the ideal door vent setting (keeps the fire going).
As a general rule, unless the fire is running very hot, it's best to leave the flue flapper all the way open.
A fire built like this will probably last about two and a half hours before requiring a refuel. Open the top firebox door, refill with lump and chunk, give the fire a good stir. Open the side door and check under the fire to make sure the airspace is not clogged with ash. If it is, rake out the ash. Close the door, and open the door vent all the way again to get the fire started. After ten minutes or so, you can return the door vent to whatever setting was working before.
Rinse and repeat as necessary until the prodcut is done, but no more chunk. The reason you're not adding any more hardwood is because small offsets over smoke meat pretty easily. Over smoked meat tastes bitter. The more you cook, the more you'll have a handle on what any given wood/meat combination requires. My recommendation is very conservative.
You could use chips instead of chunk, but you'd have to make aluminum foil packets or use a smoker box to hold them; they require pre-soaking; and they're more expensive. On the other hand, they're often more easily available in urban settings; are available in bigger variety, and it's easier to control the amount of smoke that goes into the meat. You use chips by presoaking a cup in water for about an hour, then mixing the wet chips with a cup of dry, and wrapping them in a flat foil packet of two thicknesses. Pierce the packet with a meat fork making a total of no more than eight holes, and throw the packet on top of a lit fire. A packet prepared this way smokes for about an hour, and then needs to be replaced.
The most help I can give is to leave you with this thought: NO PEEKING.
Do not open the cook chamber door for any reason the first two hours. After two hours rotate the butt and get that door closed ASAP. Then NO PEEKING for another two hours. After that, if you want to mop or spritz or interfere with the cooking method of the gods in some other way, go ahead. But minimize it. The more you mess with it, the worse it's going to be. The more you open the chamber door, the less predictable and steady the fire will be -- and the drier your product.
Hope this helps,
Rich