Many would-be DJs aren't sure whether to learn to mix with vinyl turntables or CD players. There is no 'right' answer and the choice will depend on you, but we can go through some pros and cons.
Turntables are usually cheaper to buy than equivalent DJ CD players, but that isn't the whole story. 12" vinyl singles are significantly more expensive than CD singles, so the cost advantage is quickly lost if you will buy new vinyl every week. Most dance music fans will already have plenty of CDs to mix, but if you already have a collection of vinyl it would make sense to use that. If you're clever it's possible to buy cheap vinyl records from thrift stores and other DJs, but they're unlikely to be the latest tunes.
Perhaps the biggest advantage of mixing on vinyl is the amount of control and feel you get. A good turntable and slipmat will slip smoothly while you hold a cue point, but get up to speed almost instantly. Unless you buy a top of the range Denon or Pioneer CDJ deck with a 'virtual turntable' controller, you're not going to get any tactile feel with a CD player and will need to rely far more on mentally translating what you hear into adjustments to the jog wheel. This is particularly important for hip-hop DJs who use turntablist techniques like beat-juggling or scratching.
If you learn to mix with vinyl, you'll be able to mix on any turntables in any club in the world. Turntables all have similar controls and if you can work one you can work them all. DJ CD decks often have menus and specific controls that can make them hard to operate. Most clubs use Pioneer CDJ 1000 or CDJ 2000 decks, but many don't so unless you travel with your own decks there's no guarantee that you'll know how to work their CD players. In addition, many DJs believe that the fundamental skills of DJing are best learnt with vinyl. You have to learn to control the record yourself and beatmatch without assistance from BPM counters, pitchshift controls and the like.
Access to Music
It used to be the case that dance music would come out on vinyl long before it came out on CD. Today, it is very much the opposite - it is generally far easier to get new unreleased tunes on CDR or 320 MP3 than on vinyl. A CDR is a fraction of the cost of a dubplate or a white label 12", making it far cheaper to get access to the latest cuts. CDs of course weigh much less than vinyl, so you can carry much more music in your DJ bag. If you mainly mix old-school music you're unlikely to find much on CD, so unless you've got good reason you're probably better off using vinyl. The crates are still full of vinyl records and dubbing a large collection onto CDR can be a huge amount of work.
There's just something cool about vinyl, something that says "I'm a proper DJ" when you rock up with a big box of white labels. This perception is starting to change a little, but it's still the case that lots of people respect DJs who use vinyl. On the other hand, little beats the cool factor of having the very latest tunes before they're released, so unless you're a superstar or are willing to shell out for dubplate cutting you're likely to have a fresher bag of tunes if you mix on CD
Hopefully you will now have a better idea of which format would suit you better. It is very much a personal choice and as much a matter of what feels right as anything else. If you know other DJs or live near a good DJ equipment store, try both out for size and see which one you like. Whatever you choose, the most important thing is to be comfortable and confident with your equipment.