Not so much the turntable, but the cartridge is critical. Get the best one possible.
Maybe. In the last 10+ years I've owned several decks from rebuilt Pioneers and Garrards to brand-new, entry-level offerings from U-Turn and the latest from major manufacturers.
A noisy spindle bearing, a rough spindle or even a bad drive motor will negate any cartridge. I bought a brand-new Pro-Ject 2Xperience SB (with Bluepoint No2 cart) in about 2015 or so. SOunded great for a year, then the drive motor developed a vibration that translated thru the belt and into the platter where it was clearly audible. I replaced the motor and it did the same thing within about 6-8 months. I will likely never own anothe PJ deck... but their tube/hybrid phono preamps are some of the best I own.
I replaced that deck with a Rega Planar6 (P6) with Ania cart. Couldn't be happier with it. I stopped looking at nicer decks b/c I can't imagine it could get that much better for the exponential price increase from this mid-level player. It's that good. DEAD silent operation. My main concern with a Rega (and another thing to consider that a cart can't mask) was the lack of a grounding wire (Rega use the negative side of RCA interconnects for ground) and any ground loop/hum/noise issues that might cause in my system, but, luckily, it has never been an issue.
That said, if I were jumping in, I'd get a new Fluance for the $. Seems I read nothing but great things about them and the only negatives I remember reading about them was a speed control issue when they were first released, but that was quickly remedied.
Edit: ONe more thing to remember about Deck/Cart relationship is that the better the cart, the more it will expose and even magnify the inherent issues with the deck itself.
