The standard prescription requires the use of which with non-restrictive clauses and that with restrictive clauses.

Thus:

The house, which I bought last summer, has excellent access to the lake. This would refer to the only house I bought, or at least, the only house under discussion at the moment. I am only offering additional information about the house, i.e., that I bought it last summer.

The house that I bought last summer has excellent access to the lake. In this case I am allowing for the possibility that I have bought other houses or that there are other houses under discussion. The access to the lake from these possible other houses is not of concern.

In practice you will find this rule disobeyed all the time. The minor fact that the inclusion of commas in the non-restrictive example and their exclusion in the restrictive amounts to redundancy doesn't seem to bother the word doctors. In the end, go with the old rule: if it sounds funny the hell with it.