I do studio work for national ads quite a bit, and my guitars pay for themselves - even my Private Stock models have to earn their keep, and they have all paid for themselves many times over.
Largely, which guitar to use is a matter of taste and what I sound best on. My clients seem to like my tone. My #1 and #2 guitars are a PRS PS McCarty Singlecut and a PS 20th Private Stock Anniversary Limited, through either a PRS HXDA or DG30 amp. However, I also do a lot of work with a CU24 PS, a McCarty Trem, and a 594 Soapbar, depending on what clients want.
If I only could have one guitar, and didn't have a good budget, it'd be a Core Custom 24. Totally versatile guitars that suit most occasions.
The amp is as important as the guitar. Get a good one. Wait, get several good ones.
My principal amps are PRS HXDA and DG30, followed by Mesa Fillmore and Mesa Lone Star. No clunkers allowed. I don't use modelers, others do. I've learned to be somewhat agnostic about modelers for other players. Whatever they sound best on is fine on my productions, though I prefer tube amps.
My clients understand that I'm going to use PRS Guitars, and of course, as a producer I'm my biggest client. However, others have hired me over the years to play on their ads, and I've always played PRS on them since 1991. Nonetheless, if starting out, it surely couldn't hurt to have a Strat type guitar like the Silver Sky, and perhaps a Tele.
Do you need Core, as opposed to S2 or SE? Probably not. But for studio work, I'd want S2 at the very least.
CAVEAT: I can only go by personal experience, as can anyone else. And that certainly will vary from player to player.