I would recommend Native Instruments Traktor.

The S2 or S4 are both great controllers at entry level price. They aren't standalone, so you will also need a Laptop.

Numark mixers are OK, however the cheaper entry level mixers are basically midi controllers and do not include a headphone output for queing songs.

Vinyl is great, but also quite expensive and hard to learn. Best to learn on a digital system first.