VPI turntables come with phono cables?

Do I only need regular cables like the ones that are used to connect a CDP to an amp, or do I need one of those "Y phono cables" - the kind that have a round plug with multi-pinholes in them?

You will need regular RCA cables, one for each channel. Just make sure that they are shielded. I learned the hard way after buying a pair and getting radio transmissions through the phono input.
HTH

Awesome! That's everyone for making it clear to me as to exactly what I'll need!

Can one use regular interconnects for the phono cable or does it need one of those cables that has some grounding in them attached to another small piece of wire.

you can use regular (shielded) cables and a piece of old speaker wire or the like for the ground.

I actually like the VPI cable very much after trying a bunch of others. It's shielded and has the ground wire in the outer casing too.

Sounds V good to me.