To try to answer the original poster's point - as has been pointed out, hive types do not necessarily go hand in hand with management techniques, but often they do.
Most modern conventional beekeeping is based on ideas and techniques developed in the 1850's, and over the past few years there have been a growing number of people who've been looking at "alternatives", much of it centred round top bar hives of various types (top bar hive means "no frames" - you just give them a bar to attach their comb, with no foundation, allowing them to build precisely what they want) - this tends to go with attempts to emulate techniques which allow them a less "controlled" life. For some reason which escapes me, some of the conventional beekeepers seem to be unable to stomach people "doing it differently", and can get all warp twitter and bisted over it.
In short, if you want to control every aspect of your bees' lives, and are all out for honey production as your primary goal, then you may well be happier going the conventional route, if you are of an experimental bent, and are perhaps more inclined towards a more "hands off, the bees know best" attitude, then you may be happier with what's become known as (more) natural beekeeping, whatever hive type you opt for.
The (Kenyan) Top Bar hive is ludicrously simple and cheap to build (free plans are available for download), and is an ideal starter hive - it is probably the kindest hive on the back as there's no heavy lifting, and people in wheelchairs can manage them - the design lends itself to your being able to take a comb or two of honey when they can spare it.
The Warre was designed as "the people's hive" - relatively cheap and simple, looks more like "conventional hives", but can involve more lifting, they are often run in a very "hands off" manner.
One good thing about it is that you can start off VERY cheaply - I got to 2 kenyan top bar hives, a Warre, 3 colonies, and all the gear I needed for under £150 all-in! (Ongoing costs are also very minimal, mostly boiled linseed oil for the exterior of the hives), I seldom feed, and there is no foundation to buy..........