Simple and straightforward.
My favorite! Please place bills in an envelope, card, or book for discretion.
If you prefer to avoid a paper trail while making deposits, I can accept cash at a discreet remote mailbox.
My preferred method for collecting travel deposits, and a convenient option if you'd like to avoid the hassle of cash.
You have 2 choices:
1) The easier option:
Send your PayPal payment and classify it as a gift (which waives fees for both parties).
2) The safer option:
I can send you an invoice that accounts for PayPal's 2.9% merchant fee.
While the merchant fee makes the second option marginally more expensive, the benefit is you can file a claim with Paypal if you have issues with the transaction (e.g. you can get a refund if your session never takes place). While I promise I will return your deposit if I cancel our session for reasons that are my fault, classifying the transaction as a payment for a service is a bet-hedging option I like clients to be aware of.
In contrast, the gift option (#1) is more convenient but riskier for you. This is because PayPal treats cash gifts as non-refundable, so once the money is in my hands you have little recourse if I don't follow through. Of course, I'd never do that to you — but every player defects in the last round of a game with a temptation payoff.
Is PayPal discreet?
Yes, as much as possible. The transaction will appear on your bank statement as payment for a consulting service. Googling the name of this service does not turn up anything compromising.
Please remember to be discreet yourself. Do not write comments in PayPal's comment field, even if you think they're helpful reminders. "Payment part 1/3, overnight" is suspicious. PayPal is not friendly to companions and is quick to shut down accounts that raise red flags.