You can do it "anyway you want" but there's no reason to re-invest the wheel. There's a reason that most real estate partnerships and syndications look relatively similar, with the differences typically being the economics and control.
You'll first need to decide whether you are looking to raise debt or equity. Debt is usually used for smaller properties with the investor/lender being in the first position, essentially acting as the bank. Almost no lenders will allow you to use debt for your downpayment. Debt from individuals is typically harder to raise unless you offer a very high interest rate, higher than a bank would offer. Think hard money loans.
Most RE investors are equity investors as they want to participate in the upside. The cost of capital is higher, but there is no obligation to repay if a total loss occurs, unlike a loan where you would still be on the hook assuming it's a recourse loan.
Here is the "typical" structure that can be used from small and large deals alike. I know you said you aren't trying to reach for syndication, but this can be used with just a single, or several investors.
Investors (Members) receive a 6-8% annual preferred return on their invested capital.
Proceeds in excess of the preferred return is split 70/30 (LP/GP) based upon Members capital contributions.
At the time of sale or capital event, all capital is first returned to contributing members, excess proceeds are split 70/30 (LP/GP).
It's also typical to charge an acquisition fee (.75-2% of purchase price) as well as an asset management fee (.5-2% of effective gross income).