Per the SEC you cannot solicit for private lenders. As a previous poster mentioned, if you're looking for partners and posting online, it's best to keep it vague and post case-study like figures but not directly note you're looking for partners.
Structures can be whatever you want. For instance, if you're just getting started, maybe you pay points up front + interest-only payments, annualized. If you're proposing 1 point + 10% interest on monthly payments, this is what it would look like:
1 point = $500 paid to private lender once deal is funded (or closed)
10% interest payments = $500 paid to lender at the beginning of the month
If you're doing a BRRRR- type strategy, maybe the lender's name goes on the title at close for security. You pay your lender monthly as you rehab the property. Once you sell or finance, you pay the lender back the initial loan amount.
I would say the above are pretty generous terms, but if you're just getting started, that's what you may need to offer.