Does a record player make that much of a difference??

Phono stage most important. Turntable close second. Tonearm third. Cartridge last. IMO.

Once you hear air bearings, turntable or tonearm, there's no going back. DIY if your skills are up to it. Ditto for air gap caps in the RIAA circuit.

Good luck!

@joshindc

First of all, how committed are you to records. Do you have a large collection? The reason I ask is going to the next step is not cheap and if you do not go that far you will not appreciate much of a difference.

Turntables have to meet certain requirements to " disappear." You should never be listening to a turntable. A turntable must spin accurately at 33 1/3 rpm without adding any noise or resonance while isolating the record and cartridge from the outside world. The cartridge is a vibration measurement device and it does not care where the vibration comes from. Without a proper suspension a turntable can not isolate the cartridge from the outside world. 

The least expensive turntable that meets these requirements is the Thorens TD 1600. Up from there is the Sota Sapphire with your choice of arm. Then on to the more expensive Sotas, Basis, SME, Avid and Oracle turntables. The Dohmann Helix 1 is the cream of the crop. The difference sonically between all these turntables given the same arm and cartridge is really quite small. A few of them go out of their way to look flashy which adds to the cost. You will be thrilled to death with the Thorens. IMHO it is the best value in a high performance turntable on the market today. 

Thanks for all the interesting responses.
I feel I should expand a bit on my thinking for this thread. Turntables certainly look cool and are fun to handle. And they come in all shapes, sizes and colors, and you can pretty much spend as much as you want on one (although that’s true of all audio gear). With phono cartridges on the other hand, there really isn’t much to look at as they’re so small, and they’re also fragile. Phono pre amps also aren’t much to look at. But I would venture that the sonic differences/improvements to be had by upgrading one’s cart or preamp are far greater than those found from upgrading to a better turntable/arm. Could be wrong, but my point is, I think the reason record-loving audiophiles put so much more attention and money on record players vs carts and phonostages is because there is more to look at. Not that there is anything wrong with wanting a cool looking turntable… it’s just that for pure audio bang for the buck, I have a hunch that the other parts of the analogue chain (cart, phonostage, head amp) are more critical.

I imagine many of you would disagree :)

"Could be wrong, but my point is, I think the reason record-loving audiophiles put so much more attention and money on record players vs carts and phonostages is because there is more to look at."

What? How about because turntables cost much more, for commensurate quality, than either tonearms or cartridges?  That answers the "money" part of your hypothesis.  Whether audiophiles pay more "attention" to turntables than to other components of the vinyl chain is a matter of your opinion. Got some data to back that up?

You are speculating from your presumption. The turntable and its support is the foundation for everything further down the chain. While different cartridges may have wildly differing presentations, the turntable sets the fundamental characteristics of how well the transducer retrieves the music from the groove.