Investing a million dollar inheritance for passive income

[Everett E.]

My grandfather made a small fortune in real estate and is leaving a fraction of it to the grand kids. I don't yet know how much, but for the sake of discussion, let's say I'll be getting something on the order of $1 million. As he went from high school chemistry teacher to millionaire with real estate, I figure putting it back in real estate is a good idea with the ultimate plan to travel the world on passive income for a while. 

My uncle is executing the estate which consists mostly apartment complexes in California and two pieces of commercial real estate, one in Texas (double net dialysis center) and one in Arizona (triple net bank building). My fraction of the will is not enough to cover any one property but I recently proposed that rather than liquidating everything and giving me cash, my brother, my dad, and I could split one of the commercial properties 3 ways. 

I'm leaning towards the dialysis center, as I believe that could be more stable in uncertain economic times. It's worth roughly $1.6 million and cash flows $8k a month which comes out to an annual return of 6%. If I take 35% of it, that's $560,000 share at a monthly cash flow of $2800 which leaves me $440,000 to invest other places. Notably, I'm moving to a part of the country that's experiencing a lot of growth, but still has relatively low prices (average home price is about $200,000). 

First of all, does my math look sound? Is 6% a good return? I started investing in Fundrise about 6 months ago and they've historically averaged 8-12% with a lot less effort for the investor. I guess my 6% number doesn't take appreciation into account, but what else am I missing?

This will be my first foray into real estate, with the exception that I'm going to try to buy my first home before the will gets executed (hopefully by the end of the year). I see a lot of potential in my new city, and I like the relatively hands off approach of commercial real estate. Should I try to stay in this niche, or diversify a bit into single family or multi-family units?