Australian REITS have been an awesome investment over the last few years - I have had significant out performance from them. However, I can't help but feel they are pricey at the moment, and the things that have helped them (loss of trust after GFC and lowering interest rates) are now fully priced in.
Be aware that REITS cover a lot of different asset types, from office buildings and shopping centres through to self storage units and data centres. If you don't want to put the research in but want general listed property exposure, consider a REIT ETF, such as SLF or VAP.
I've been happy to buy REITS direct, as much of my day job is about providing services to the commercial property sector, hence I've been a stock picker.
REITS I own are:
AJD - owns data centres
DXS - offices and industrial
GOZ - office and industrial
GPT - Office and Retail
SCG - Australian and NZ retail
SGP - mixed + residential
SYD - airport
UOS - not technically a REIT but a malaysian property play
VCX - Australian shopping centres
WFD - international retail
Depending on how liquid you need to be there are also unlisted commercial property investments, but most need you to qualify as a wholesale investor (2.5m in investable assets or $250k/year income)