Congrats Steven. Good question!
For private money (friend, family, etc)
In the end, it's whatever the partner will agree to. Some might want equity, but others may be happy to just make a loan. You can negotiate anything.
For non real estate investor partners, consider their alternative options, and be in range. If they can make 7% in the market, you need to do better than that otherwise they should just start in stocks. I usually shoot for loans. Make sure everybody is winning or there will be no takers. If somebody wants equity, I give them the corresponding ownership. If they put in 5% of the ARV, they get 5% ownership. It doesn't have to be that way--you can give whatever equity you want for the money you receive, sweetening the deal for you or the investor. Just be sure to stay cash flow positive and not to give up so much it's no longer worth it for you!
For more formal partners, hard money:
They will want to see the deal and all the numbers that go with it. Usually you want to try and get a relationship with one of these first so you know what they are looking for. Hml are shrewd... Be careful especially if you're new to that.
Let me know what happens! Looking forward to hearing other people's thoughts as well!