Three. Freaking. Cheers for this one. Anyone who's had to suffer through MySQL's abysmal attempt at doing "spatial" should give PostGIS a well deserved look. I've used Oracle Spatial, ESRI's SDE (which rides on top of MSSQL/Oracle/DB2/SyBase) MySQL 'spatial' and PostGIS. I have to say, hands down, PostGIS has been my favorite. We had to implement MySQL spatial as all of our tabular data was already there and the IT folks felt "comfortable" with it as they knew they could dump it to a plain text file full of CREATE statements any time they wanted to. The problem we have seen is that dumping some of our ancient MySQL spatial tables, we could not import them into other versions. And vise-versa appeared to be true as well. (I'd need to go back and look)
You and your IT folks may be interested in Spatialite, which sounds like a good use case for what you've described. Spatialite is spatial extensions to SQLite, means you can store spatial data in standalone DB files. Has good level of support in GIS software, plus it's the first spatial database format to support the upcoming GeoPackage standard (due to replace shapefiles):
http://www.gaia-gis.it/gaia-sins/http://www.ogcnetwork.net/geopackage