DJ Gear for beginners

If you want start DJ-ing, you need a few elements to start with:

Controller set-ups: Rekordbox & Traktor

Don't want to spend too much money? Want an easy laptop interface? Do the venues/parties where you want to play not have their own DJ gear?
Then you can go for a laptop & controller setup. I recommend a Native Instruments Traktor Pro 3 or Pioneer Rekordbox set-up.
The software comes for free with the gear that you buy.

Rekordbox:

Traktor 3:

Stand-alone set-up: Pioneer (Rekordbox)

I recommend a Pioneer DJ stand-alone setup (supported by Rekordbox software, which you need for music management) if:

I teach with any of these set-ups!

What hardware do these setups use? More info below!

Gear recommendations

Depending on your budget and aspirations, I recommend the following gear. Most things are for lower budgets / beginners, but with a minimum good quality (no shitty stuff). Where to buy? These are some great web-shops in Netherlands/Europe:

I don't recommend Media Markt! (BAD returning policies)

Buying second hand? Get it from a trusted source and/or go with someone experienced and test stuff thoroughly!

Controllers for laptop

Stand alone setup

A stand-alone setup is either 1 device that does everything (players & mixers in 1 thing), or individual mixer & player units.

Headphones

Speakers 

Any pair of studio monitors will do, it's really budget dependent if you want to have richer sound. If you already have any kind of speakers, you can try connecting them.

Good cheap options:

Richer sound:

Don't forget to buy audio cables to connect your DJ gear & laptop to your monitor speakers. You also might need pads or stands. Ask the web-shop for help if you need it (they are kind).
For the best audio experience, set up the monitors in your space according to their instruction manual. The general rule for DJing is to set them up approximately at ear-height, somewhat pointing towards the ears, from around 75-100 cm.