Godzilla-thon: The Millenium Series (1999 - 2004)
The Millenium series as a whole was a little better than the Heisei series, but only in the special effects department. There were times where CGI did not look right, however there were other times where it really does show improvement with each movie. This was both a good thing and a bad thing. A good thing is that TOHO is really trying to get with the times and push themselves to explore different styles of special effects. The bad thing is that it was a settle hint that years later, it would almost be an end to the tokusatsu style of practical effects. As much as I do like the cheesy man in suit and miniature model style of the movies it almost always put the suit actors at risk from constantly passing out from exhaustion or near death (Yes, there were actual times where suit actors almost died on set). Also, using CGI is cheaper because it is less time consuming having to redo a certain scene just because a building didn't collapse the way it was intended to or not having to worry about a suit malfunction. So I am more for the good side of it more than the bad.
My recommendation list is going to be different for this one. Since there are not that many movies in this series that I would really recommend I am going to do a list in order from most - least liked movies. I hope this helps. Note: I am not putting Tri-Star's GODZILLA on the list because it isn't part of the millenium series.
Best -> Least Favorites:
Godzilla, Mothra, King Ghidorah: Giant Monsters All Out Attack
Godzilla: Tokyo S.O.S.
Godzilla Against MechaGodzilla
Godzilla: Final Wars
Godzilla vs Megaguirus