what you are describing is known as GPS Tracker software. There are lots of freeware (http://www.freewarepocketpc.net/ppc-tag-gps.html) and open source projects enabling GPS tracking on Windows Mobile (5) devices. What about this (http://gpstracker.codeplex.com/) for example?
If you intend to write your own software you can simply save location data into a plain text file or in a standard GPX or KML format. Using a database engine like SQL Server compact (SDF files) looks oversized to me.
On the PC side you can use Google MAPs API with the saved data (GPX or KML). See also GPSbabel to convert between these standard formats.
regards
Josef