There are two types of charcoal - lumpwood and briquettes - each with its own pros and cons.
I'll try to keep this discussion on the practical side rather than getting too much into Wikipedia territory on the subject of charcoal manufacturing.
There are two types of charcoal available to the barbecuer.
Lump charcoal is the stuff that looks like it is made from small logs.
This process is something like 5000 years old and was developed as a way of heating metal for smelting at the start of the Bronze Age no less.
Today, lumpwood charcoal is usually made from scrap wood from timber yards, flooring manufacturers and other places where wood is used in manufacturing.
Lumpwood charcoal generally burns hotter than briquettes - I mainly use it for direct grilling of steak or burgers etc.
Although it burns faster and hotter, it's easier to adjust temperature by spreading the coals out more or piling them up, or adjusting vents, etc.
Usually lumpwood is more expensive than briquettes are.
These are a more artificial product than lumpwood. They are made from sawdust, bark, and leftovers from the paper industry.
These constituents are chopped into a uniform size and roasted in a kiln, then formed into the uniform briquette shape we recognize.
They are cheap to buy and produce a more consistent, but lower heat over a longer period of time than lumpwood.
One downside is the amount of ash left over; the other issue is the performance enhancing and binding additives used in their manufacture. In actual fact it is unlikely that there is much that is harmful in them - otherwise, presumably, products would be banned in most health and safety obsessed Western countries.
The list of ingredients on most briquette bags will likely be made up of natural things - like sawdust, limestone, coal, charcoal made from bark, sodium nitrate and not much else.
Very cheap products may have some kind of petroleum based additive in that might produce a "chemical" smell during cooking. But otherwise I don't think there is anything wrong with charcoal briquettes at all - just go for quality, as with anything else.
Purists might argue that lumpwood, being an all natural product, is superior in performance and taste. But, the only practical downsides of briquettes I have seen is the time they take to light and the amount of ash they produce.
Personally I buy both and use them for different tasks, lumpwood for direct grilling and briquettes for indirect barbecuing and smoking - mainly because they burn longer and slower. This is just my preference.
Either way if I can get them, I use charcoal products certified by the Forest Stewardship Council which hopefully guarantees that products are made from properly managed forest sources.
Or consider buying them from a smaller local dealer, there will certainly be one willing to deliver to you. If you are in the UK, I can recommend Liverpool Wood Pellets - In the US see below.
Buy the best quality and local as possible if you can. Otherwise, go for quality.
If you want it delivered to your door, Amazon stock a large number of really good charcoal products:
Kebroak hardwood charcoal is Amazons best selling charcoal product
Bags come in four sizes, 5lb, 10lb, 20lb and 40lb - the 40lb bag is around $45 at the time of writing.
Also not that this is billed as being restaurant charcoal, this means it is a product aimed at restaurants - who won't use any old crap - and tends to consist of larger lumps that burn hotter and for longer.
In fact if you look at the Amazon reviews, there are several from professional barbecuers who rate it highly. Fogo is another good choice and is a very similar product with equally glowing Amazon reviews.