Can someone tell me what parameters I need to use in Handbrake in order to get the correct mp4 file.

That depends on what size you want. But here is what I use for Full HD. 

Under Summary:

Format: MP4 tick passthru Common Metadata

Tracks: H.264 (x264). Same as Source FPS VFR

             Audio: AAC Passthru

Filters:  Decomb

Size:     1920x1080

Dimensions: Cropping None, Resolution Limit: 1080p HD, Anamorphic: Automatic Scaled, Size: Optimal Size

Filters: Deinterlace: Decomb preset default

Video: Encoder: VP9, Framerate (FPS):Same as Source, Variable Framerate

Quality: Constant Quality: 22 CQ

Audio: AAC Passthrou (This depends on what you are using)

Hope this helps