Shade
I have taken to shuffling the cards myself, fanning them and asking them to choose the seven/four/ten needed for the spread. It means I have no deck anxiety and they are involved in the process.
It depends on the deck. I have some that I use just for myself. I also have others that never leave the house because they're OOP and/or rare.
My go to deck, even after all these years, is the regulation RWS. I use it for public readings, too, as that deck is what people associate with tarot above all others. I'll use other mass-market decks like the Aquarian, Morgan-Greer, Hanson-Roberts, etc. for public as well as private readings too. If someone spills a drink on them, they're easy to replace and I just tack the cost onto their fee. No biggie.
If you've only got one deck, then you'll be using it for both public and private readings by default. If you have multiple decks, do what you feel is best! There are no right or wrong answers here.
I go to a cartomancer for personal readings and she does ask her customers to not only bring their own deck of playing cards along with them for the reading, BUT she also asks you to carry said deck on you for awhile (the longer the better) to pick up your energies. She also warns you against allowing others to handle said deck as she picks up on the energy from the cards when she reads. So, its a combination of a card reading, psychic and medium and an empathic reading in one. However, if you do not have a deck of a cards, she has a few in her reading room to lend out to you--and she will also do a phone reading using her own cards while you participate on the other end using your own cards.