1. Gigan - My favorite which is why he's first. Like jelly said, if this turns into a series I would prefer it to became progressively more "out there", so if they eventually tackled alien invasions he would fit right in.
2. MechaGodzilla - Of Godzilla's "big name" villains, MG is my favorite, before Ghidorah and Mothra, which makes him second on the list. Alien origin or man-made, either would work for me. The former would feel more refreshing after the Heisei and Millennium versions of the character, but if we'd get space monsters in the form of Ghidorah, Gigan, etc. in this series the latter would probably be more appropriate.
3. SpaceGodzilla - I'm relatively alone in this I know, but he's one of my favorite kaiju, I just love the design, and there's potential in his powers and being a "Godzilla clone". His movie wasn't the greatest, which is exactly what would make it exciting to see him used to his full potential. If the origin story is too ridiculous and/or convoluted they could easily alter it, like Toho has done so many times in the past.
4. Megalon - He's a cool, fun monster that's very underused. Would be awesome to see him paired up with Gigan again, as a homage to Godzilla vs. Megalon. Hopefully both of them would retain their personalities and dynamic they have together.
5. Mothra - I love Mothra, so I had to include her. If they want to work some of the more popular and recognizable monsters into the sequels then she's a solid choice. Some fans argue that she's "too weak" to be a proper foe for Godzilla, but that's stupid; regardless of how she's been portrayed at times in the past she can still be plenty powerful and fearsome, it just depends on how the filmmakers choose to portray her.