You may draw points, lines, and polygons (square/star/rectangle/free shpae) by using OL3. Please see following link: OL3 Draw Examples
Or if you find OL3 is too complicated for you, please try Leaflet.
However, I personally prefer OL3.
If you can build some background program to access the GPS coordinates constantly, and write them into GeoJSON file, you may be able to update the GPS points and draw lines on the OL3 maps by reloading the GeoJSON every one/two second(s).
I am no master, but hope you will spend time to do some researches next time.