I'm still pretty new to this stuff, so bear with me. In PostGIS how could I find a polygon that would contain all the linestring records in a given table?
If you know beforehand what your polygon is, you could do:
There are many ways to fetch the polygon you want, but the path is to try for ST_Intersects = true
OR do you need the polygon that encloses all linestrings?
If so, you can use ConvexHull: