Before starting a career you need to know what sort of DJ you want to be. If you're not in to music much, then it probably isn't the career for you. For this website I have split the DJing types into 2 main categories: Mobile/special events DJs and pub/club DJs. Both styles of DJing require that you have access to a relatively large selection of music.
To do any DJing there are only few essential items you really need. The traditional setup used to consist of two record decks and a mixer but these days a lot of DJs use dedicated controllers plugged into a laptop or a "Digital Vinyl" system (which still use a turntable but with a special control record). At the high end, several Manufacturers have their own hardware based media players that can play digital music files without a laptop, but require a dedicated mixer, such as Pioneer's CDJ2000 NXS2 and Denon's SC5000. When starting out you could just use the DJing software on it's own (both Traktor and Virtual DJ have a software based mixer). There's also a wide range of basic controllers such as Pioneer's WeGo 4 and Numark's Mixtrack decks that are perfect for learning the basics of DJing. With the advent of digital music DJing is much more accessible that it has ever been. Back in the day the basic setup of 2 vari-speed decks and a analogue mixer would set you back hundreds (or thousands if buying Technics 2010s).
Unless you are only playing in larger pubs or night clubs where most equipment is provided, you will also need an amplifier and speakers - often mobile DJs and pub bands will use speakers with built-in amplifiers known as active speakers - these save you the hassle of carrying a separate amplifier everywhere you play, but tend to be more expensive. When starting out, the auxiliary socket in the back of most stereos will give you a basic amplifier and speaker setup.
Practically all music genres are now available in a digital format, but this didn't used to be the case. More niche genres such as Drum & Bass and UK Garage tunes used to only be released on vinyl - bear this in mind when trying to build up a collection of throw-backs/classic tunes. Some well known bootleg mixes (mashups of two tunes) were only ever released on unofficial "whitelabel" records and will never appear on iTunes/Beatport/Traxsource/Juno
Before playing to the public, it's a very good idea to practice and refine your skills first. There is probably nothing worse than screwing up your first gig, as this is likely to dent your confidence and put you off DJing in the future. Provided you enjoy DJing and enjoy buying music, then with plenty of practice there's no reason why you can't become a successful DJ and make a living from what you enjoy doing. Even if you're not making a living from DJing, you can still do it alongside your day job, as nearly all gigs are in the evenings.