Do you have to use the PS Move Motion Controller on this game or can you use the standard controller instead?

You can use either PS Move Motion Controller or standard controller. I use standard controller just like PS2 G1 Jockey. Personally, I feel the music should be a bit more upbeat than soft tone. Good thing same strategy still work: Front runner whipping around 1.5, Start Dash around 1.7-1.8, and Last Spurt/Stretcher runner around 2.2 length. ^_^

Will this work with PS4?

Sadly, Champion Jockey will not work on the PlayStation 4. I am hoping PS4 will release a horse racing game in the future but in a small market for these types of games, it seems doubtful. I own this game along with several of the PS2 Gallop Racer series of games. I would recommend Gallop Racer 2001 and 2003 for ps2 if you haven't played them before and have a ps2 to play them on. Hope this helps.