Most of the better private equity managers require initial subscriptions on the order of $1-5 million. For the very best known (eg Sequoia) there's a line and you ain't getting in soon.
Despite all the fees, private equity *is* further out on the efficient frontier, so it does let you capture the liquidity and volatility premia. You're usually locked up for 7-10 years.
Private equity is still equity, though, so will usually follow the stock market with greater volatility and a year or two lag.
With real estate investments above a few million you can buy into commercial buildings, housing developments, apartment complexes etc. That is, different things with different return streams than if you're just buying houses.
So a few million to PE, a few million to RE, each maybe 10-20% of your portfolio gives you an overall portfolio size north of $10 million (your answer). You're dealing with multi-family offices here. Below that just pick your allocation and index.
Hedge funds... most of the larger funds nowadays are primarily vehicles to make the managers rich. Source: used to work in the business.