A rookie with 10K, seeking advise

Replace the Lintons with either Legacy Signature III or Focus.  Both are high efficiency speakers that only need 35 watts (but good current) amplification.  They cost between $1500-2200 (Sigs) to $2500-3000 (Focus) used.  Big sound, big dynamic range and excellent frequency range.   GroverHuffman cabling (high end at moderate cost).  Used gear galore to use with those speakers.   Used VPI turntable/arm with a Dynavector 20X2 H cartridge for the table which will work with a wide range of MM phono stages.   A Denon 1500 or Kyocera 310/410 CD player for a few $100s.  Under $10K easy to get great sound, used.   Room treatment/power to equipment though will make a big difference   Stick mostly with solid used equipment at a big discount to new (except for the cartridge).  

@gwilmot  I'm still using the two pairs of speakers I recommend.  Also the L version of the cartridge and a Kyocera CD player for the second system.   So you are wrong in a blanket assertion.

Someone mentioned an Ortofon Black cartridge.  The MM cheapest version is great on about 15-20% of records and yuk, off sounding on the rest of one's collection (My friend had one for six months and could not take the majority of his discs sounding bad).   He is using an AudioTechnica (especially nice on mono LPs as well) and a Denon 160 instead.