Gary Gygax originally used miniatures for reenactments of actual battles. Eventually, he added a medieval flair and then some fantasy elements. Chainmail was born. This evolved into Dungeons & Dragons (Basic Rules), Dungeons & Dragons (Expert Rules), Advanced Dungeons & Dragons, Advanced Dungeons & Dragons (2nd Edition), Dungeons & Dragons (3rd Edition), Dungeons & Dragons (4th Edition) and an offshoot: Pathfinder.
All of these still have a following. Each rule set has elements that are attractive to different groups. Most people are convinced that the version they play is the best but all that can be said for sure is that they are all distinctly different from one another.
Fourth edition is the newest and a lot of people, especially those new to the game, go with it solely for that reason. Version 3.5 has been made available as a completely free download through the Wizards of the Coast website. Free reference materials sway a lot of people and many go to v3.5 solely for that reason. Others go to one or the other of those two for entirely different reasons. Whatever reason drives them there, 4e and v3.5 combined constitute the lion’s share of D&D players. Pathfinder is a cross between the two and has a large following as well, with the early versions coming in after that.
How Do You Choose One Over Another?
That is entirely up to you. As I said, there are aspects of each version that appeal to different groups. You need to look at them yourself and determine what system you prefer.
First off, avoid the Wizards of the Coast forums until long after you have made up your mind. The version wars are still going on and everyone loves one and hates the other. Evaluate them for yourself before being subjected to that.
If you are new to D&D, I would suggest downloading v3.5 and reading through it. Since it is free, I think that is the best place to start. Once you have gone through it thoroughly go to the local bookstore and sit down with the 4e Player’s Handbook. Pick a store that doesn’t mind you leafing through the book for an hour. Read up on the differences between the two systems. They are very different so the more you understand v3.5 first the better equipped you will be to see those differences and evaluate them.
Just to give you a point of reference as to the cost of the books, 4e has three books (Dungeon Master’s Guide, Players Handbook, and Monster Manual) that constitute the core books. These three are absolutely necessary and run $20-35 each. There is a follow-up book to each of those out now for another $20-35 each. Player’s Handbook III is coming out in a few days, with Monster Manual III and Dungeon Master’s Guide III coming out later this year for an addition $20-35 each. There are another dozen books out there now that are useful to have, with more on the way, all of which are also in that price range. In short, books alone will cost you a few hundred dollars. That’s why I suggest starting with v3.5 for free before committing. :)