I own two REITs that total 6.5% of my portfolio. Here is what I do personally, but your mileage my vary.
I stay away from VNQ. I'd rather pick one or two companies that are specialist in specific property types that I find to be an acceptable risk profile relative to their return. I can look at the properties they own, who the tenants are, and how much debt the REIT carries against their portfolio. I used to be a commercial lender so I'm pretty familiar with looking at this stuff. Similar to buying actual real estate properties, you have to be price disciplined on buying REITs. A good REIT can be a bad investment if the price is too high. Personally I think names like American Tower and Public Store are trading at insane valuations and I don't want to own them. Great companies, horrible valuations.
The names I own are EPR and STAG, but all in I bought them at more than 20% below the price they are trading at today.
If you want to own REITs, put together a list, do your research, then decide what your required return is. Then sit on your hands and wait for the market to go so haywire and buy. REITs can be driven down overall by either the stock market going down or by interest rates going haywire. I've only been investing in them for 10 years, but it seems about every twenty four months a good deal shows up.
If we're in for a lower return for longer period of time, some of these names are a decent risk adjusted return in the mid 5% range.