Any recommendation as to investing in which type of REITS if I'm willing to invest somewhere between $5-$10k?

Long Short, invest in REITs that you have more knowledge on.

Best is you are one of the beneficial/clients/indirect users of the REITs itself.

So you would have the best knowledge of the REITs moving forward.
However, I would strongly recommend to pick up this book before investing.

https://www.goodreads.com/en/book/show/17883242...

Can find this book in the National library too.

http://catalogue.nlb.gov.sg/cgi-bin/spydus.exe/...

What is your required rate return

In general, single country REIT is higher risk than multi-country REIT.
However, there is currency risk if u buy multi-country REIT

Similarly
Specialised REITs are harder to find new tenants than general REITs so that affects Yr choice

Industrial >hotel> shopping mall