That is a very hard question to answer. OpenLayers 2 has been very successful and it is easy to find examples for just about everything. OpenLayers 3 is a total rewrite and uses the Google Closure toolkit which provides a number of useful services: code compression, event handling, cross browser support, etc. OpenLayers 3 also uses webGL rendering, when it is available, which provides super slick raster and vector rendering and (soon to come 3D virtual world integration via Caesium).
The main negatives of OpenLayers 3 at this time is that there are less examples and less people with skills to help others out, either on irc, Stack Exchange sites, mailing lists, etc, though this will change quickly with time. I also think that the learning curve is probably steeper, but that it will be more powerful and easier to extend once you have made that step.
OpenLayers 3 is a total rewrite, just to be clear, so while some of the concepts will transfer from 2 to 3, tiles, geometries, layers, you will have to start again with 3.
I am tempted to say that for a beginner you should go with OpenLayers 2, but my head says OpenLayers 3 is the future, and to go with a little more pain now for a lot more gain later. Sorry, such an question is bound to produce a sitting on the fence answer.
The boundless blog has some great information on OL3 that might help you decide. EDIT: As noted by Gabor, the Google Maps example does not use Google Map tiles directly, but embeds a Google Map div in the page, and this will not change, unless Google change their policy on tile usage.
Note, about Mapserver: this is server platform that will produce data in a number of formats, vector and raster, eg, WMS, WFS from a number of sources. So, you will not find examples that deal with Mapserver directly. Instead search for examples that use WMS, WFS, and load your Mapserver details as part of the source. The same applies to Geoserver.