Out of those? PRS. Hands down.
IMO the PRS SE will have the most familiar "feel". They have great quality and sound. I've never played the ESP, but I hear good things about them.
I owned a PRS SE Santana and it was excellent. Because of the shorter scale it sounds more "Gibson" to my ears.
I've had an Epi and a Vintage. The Epi felt cheap, the back was mahogany veneer on some unspecified wood, I sold it on. The Vintage feels and sounds like the real deal and isn't going anywhere.
The PRS SE guitars rival most USA made products in terms of quality and feel. It is pretty spectacular, actually.
Sure, some of the components represent a compromise but the bones are almost always solid.
I am not a fan of the feel of an LP even though that is all I played when I was younger. But nothing but an LP sounds like an LP. The PRS will sound like a PRS.
I think the Epi or Vintage will be your best bet if you want a Guitar that sounds like an LP. The other two are very well built guitars, and will approximate an LP sound.
I love the sound of an LP, but can’t get along with the feel of one as mentioned above. I have settled on a Schecter C1 Plus and an old Ibanez SZ to get my humbucker sound. And looking into getting a Schecter Solo as well. The Ibanez is closer in sound, but just not there. A true LP has a thickness and bottom end that other guitar designs just can’t produce. I owned a PRS Tremonti at one time. It was a great playing guitar, very well built, but heavy and did not sound like an LP. Also owned a G&L Tribute ASAT Carved Top that came very close as well. Very nice playing and well built guitar for little money.
I would suggest getting out and playing a few if you have that option. You might be ok with the PRS as others have mentioned, which is a well built Guitar. This is just my opinion on my experiences and use it just as that, just an opinion. Good luck with your quest.
I went down this same path last week. Theres a thread below on it. The PRS while nice didn't do it enough. The humbucker Revstar was as close to the LPs as I could find. (But I already have one). I ended up with a Studio. It's great.
I love the LTD Les Paul-type guitars.