I think one can put together a very nice sounding system for $3000.
My thoughts toward accomplishing this: 1)Stay away for speakers that are difficult to drive. Think quality over quantity power. 2) Purchase a line level integrated amplifier. Purchase this component used. 3) With vinyl the TT, arm and cartridge contribute greatly to the presentation. Stay with a MM cartridge and phonostage. I would allot at least 1/3 of budget to these components. Used is also a good option for phonostage.
More information as to room size and listening habits would prove beneficial towards getting more specific recommendations.,