The problem with recommending a vinyl entry point is that there are even more variables than you've got already, just to get a sound from the system: t/t, arm, cartridge, preamp/headamp, cables. Oh yes, and then you've got to get the right turntalbe support/shelf/rack, and then you've got cartridge alignment, tracking force, (vta anyone?,) and dirty styluses. And mat material and....
Hence everyone's recommendations of, say, a Rega or a Project as an entry point. If you want any more and are undecided as to whether you should enter the world of vinyl, then you've got to go an do a LOT of listening before you take the plunge.
2nd hand gives you stunning value. I recommended/found a second hand Linn LP12/Ittok for my brother-in-law (21yo) from Loot, which he loves, and gives a wonderful entry point. But you've reached the stage where you care about the nuances of the sound you're hearing, and the Linn sound may not be one that you like.
In the house my son's got my dad's old Thorens TD160 and I've got a 2nd hand Rega Planar 2 which I bought while I'm (still in the middle of) restoring my 20+ year old Oracle/FR64s/Koetsu Black. I've still heard very few realistic CD players, hence my presence in a forum like this, to learn from others' experiences whilst still being capable of affording the equipment. I love vinyl, but it's very easy to dislodge a vinyl system from its state of loveliness (read the lists in the 1st paragraph), and you might not like the faffing about and the increased exercise every 15-20 mins.
And, as someone said earlier, the quality of 2nd hand LPs can be dire - scuffs, pet hairs, emulsion paint (!) and the rest. So my two recommendations to anyone considering vinyl - a good stylus cleaner (I still use my old Audio Technica ultrasonic thingy) and build yourself a vacuum record cleaner.