First of all, you should realize that investment returns over a 3-5 year time horizon are not very large. Open up Excel and check out the results of the following:
=1000*48 (principal from $1000/month for 48 months)
=FV(0.05/12, 48, -1000) ($1000/month for 48 months at 5% return, compounded monthly)
=FV(0.1/12, 48, -1000) ($1000/month for 48 months at 10% return, compounded monthly)
spoiler alert: each of the above is only ~$5k higher than the previous one. Weigh that against the risks of a volatile stock market.
As for REITs specifically as a savings vehicle for real estate, I've seen this advice:
http://www.obliviousinvestor.com/using-reits-to-save-for-a-down-payment/