There are generally four different places you can buy bikes, not all of them are good:
Catalogues -
This is where you buy a bike unseen, from a mail-order catalogue company or one of the big catalogue stores. The bikes arrive disassembled and packed into a box. The bikes are generally pretty cheap, as the company does not need to hire anyone to assemble, check or fix the bikes - you do that for them. Warranty problems can be tricky, though, as you are often dealing with a company a long way away which does not have any bike experts on it’s staff.
Non-bike stores -
These are places which do not specialise in bikes, for example garages, department stores, toy stores and supermarkets. Like the catalogue companies, they do not have any bike experts on hand, and usually your bike comes packed in a box. If it has been assembled, ask yourself: does someone who has been trained to stack boxes of cornflakes have the skills to make sure a bike is safe? The only advantage with buying from these companies
over the mail order catalogue type companies is that when you do have problems you can go complain in person.
Chain bike stores -
These are companies which have a chain of stores selling bikes, usually alongside other things like car parts. They do often have trained staff, and your bike should be properly assembled and safe. These stores can afford to keep large stocks of the most popular bikes and parts, but are not particularly cheap. Their staff, while trained, do not usually have the breadth and depth of experience needed to deal with the more complicated problems some bikes raise.
It is worth mentioning that the quality of service available at these types of
outlet varies dramatically. Some stores have very good, keen personnel, but
sadly the majority are staffed by chimps.
Internet Only Bicycle Dealers -
With the increase in popularity of internet usage, a number of specialist online sellers have emerged. The number of places where you can buy a new bicycle on the internet is on the increase and these range from sites which only sell bikes and accessories to those with a wider product range. A number of real bricks and mortar stores have websites from where you may purchase, but in addition to these there is an increasing number of internet only bike shops. The service these sites offer varies in quality, with some being operated at an extremely professional level with genuine stock holdings and dedicated staff, but there are also a number which are operated more like hobbies, often from somebody's bedroom. Talk to a real live person to ensure that you will be getting what you pay for. Also be prepared for the possibility of dissatisfaction resulting from possible damage caused by delivery companies!
The single biggest issue when comparing bikes bought from the internet and those
available in local stores is the condition in which you will receive your bike.
Again, standards vary, but ensure if you are buying on price alone, that you are
comparing like with like. It is incredibly difficult to ship a bike to a
customer 100% fully assembled. Indeed, some assembly will almost certainly be
required when you receive the bike. The best online only suppliers send out
bikes such that all you will be required to do is to turn the handlebars,
tighten the stem, screw in and tighten the pedals and adjust the saddle height.
Unfortunately, many don't and send out bikes pretty much exactly as they receive
them from the manufacturers/importers. A skilled mechanic will, on average, take
around 1 - 1½ hours to fully assemble and make a bike safe for the road.
Now whilst we wouldn't try to claim that assembling a bicycle is like rocket
science, it isn't something that you should undertake lightly. You could take
the bike to a local bike shop, but expect them to charge very heavily for the privilege
of having your bike set up correctly. Many bike shops may even refuse to set the
bike up for you. Consider the costs of assembly and the possibility of the bike
not being roadworthy when you compare online prices with in-store prices.
Independent Bicycle Dealers -
These are independent companies and can range from your small local bike shop to large companies with several stores. IBDs generally have the best-trained staff, with years of practical experience. Larger companies have huge stocks of bikes and parts, not just the most popular ones. Smaller IBDs do not have the space or finance to have huge stocks of bikes or parts, but most are very willing to order something in for you if you ask. Many IBDs specialise in niche markets, selling bikes and parts that no-one else does. For more information on finding a good independent bicycle dealer, have a look at the Good Shops page