Here's a quick look at some gear the Beatles used...and the modern day equivalents
The Beatles used a wide variety of gear, which more or less changed according to each "Beatles Era". Of course, due to their popularity, The Beatles were responsible for popularizing many brands such as Gretsch, Vox, Epiphone and Rickenbacker.
The Cavern Club/ Early Years
In the early days, the Beatles used almost exclusively Vox Amps, both the AC-15 and AC-30, which are the obvious choices if you want to have the classic beatles sound. You can't go wrong: get an AC30 and either a Gretsch Country Gentleman like George, or a Rickenbacker guitar (such as the Rickenbacker 330 or Rickenbacker 360 models.) It's interesting to remember that originally, in the pre-Ringo days, John had a Fender Tweed amp, like the one below:
The Paul McCartneys out there can't have anything other than a Hofner Violin bass, just like Macca's! Hard not to feel inspired when you play one - no wonder Macca chose to play this model: he was originally a guitarist, and the narrow, slim neck of a Violin bass is much more "playable" than most other basses. Epiphone has also some truly wonderful John Lennon and Paul McCartney -style acoustic guitars: The John Lennon J-160E wass a great copy of the J-160E that John used in so many classic beatles recordings (and gigs). It's been discontinued, but the new, Limited-Edition EJ-160e is just as good!
The Paul McCartney used to play an Epiphone Texan, which he used for "Yesterday". Let's not forget Ringo, though! Owning a Ludwig Drum Kit is a must if you want to have a similar setup.
Those more interested in the Fab Four later days can also find plenty of interesting gear. Firsty, we'll have to move away from Vox amps and go for a Fender.Try a Fender Twin Silverface for that Abbey Road sound or, if you're on a budget, a Fender 68 Princeton Reverb will do, for classic Fender tones and reverb. Guitars? Well...there's plenty to choose from: George used a Gibson SG on "Revolver", a Fender Stratocaster, Gibson Les Paul and finally a Fender Telecaster for the Let It Be Sessions. Several models of all those guitars are available. Both Lennon and George were never too far away from a semi-acoustic guitar though, and the most notable were certainly the Epiphone Casino the classic Hollowbody guitar with hot P-90 pickups. Thanks to The Beatles, these guitars continue to be very popular choices! George also played a Gibson ES-345 for a while, so you'll probably do fine with any good semi-acoustic such as the Epiphone Dot sunburst.