A VLOOKUP function would work, but I prefer the flexibility of an INDEX/MATCH. The way that is set up is pretty straightforward. It would look something like this...

=INDEX({Sheet 1 Range 1}, MATCH(Property@row, {Sheet 1 Range 2}, 0))

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{Sheet 1 Range 1}: Cross sheet reference where you would select the entire column on the first sheet that holds the information you are wanting to display.

Property@row: The cell reference to the column on your second sheet that houses the property name.

{Sheet 1 Range 2}: Cross sheet reference where you would select the entire column that holds the property names.

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From there you would just update the first range to reference the appropriate column in your fist sheet for the data you are wanting to display ({Sheet 1 Range 1}). Everything else would stay the same.

There are a few other ways to increase flexibility, but this would be a pretty straightforward approach that will allow you to rearrange the columns and sort the rows on both sheets without having to worry about breaking anything like you would with a VLOOKUP.

It definitely took me a little while to get used to the thought process behind INDEX/MATCH, but once it clicked it made life so much easier. 

And you are most certainly correct about using the 0 in the MATCH statement.