Swagger and braggadocio aside, the purpose for those "big" speakers is so that you have a true sense of how the music sounds.
Granted for you to get the best from the "big" speakers, you need to be working in a treated room (a room adapted to have a flat frequency response at your primary listening position).
Multiple speaker setups are also useful in determining the transparency of your mix - each type of speaker brings with it its own colouration to the source signal (cabinet resonances and design compromises are the two big things that affect the freq response of a particular set of monitors). In addition, any powered speakers are likely to colour the sound as well based on amplifier design philosophy - single amp with passive crossover (soaks most of the power and the transfer characteristics will alter the way the sound is projected) or bi-/tri-amp for individual drivers in the cabinet after an electronic crossover, which may introduce its set of phase shifts and frequency colouration.
A laptop cannot compete with a properly spec'd computer with reservoir based fluid cpu cooling.
Multiple screens help to move your on-screen views into manageable view areas
Headphones will barely cover the needs of your mixing, as they are incapable of reproducing bass freqs reliably or colour free (they do not have the diaphragm size to accurately reproduce low freqs - this is related to wavelengths of these low freqs which are in the multiples of feet - 20'+ for freqs below A[SUB]0[/SUB] (55Hz) (the pitch of the A string on a Bass and a bass guitar).
General consensus is that a pair of beats by dre are no better than any standard issue headphones from most of the headphone manufacturers - why pay extra for the badge and name if they are no better than something far cheaper????
In the end, it is down to you, but skimping on quality gear at each point in the production means that you are prepared to skimp on quality before you begin to create, not an auspicious attitude to have towards your creative endeavours