Whats the best way of this type of movement?

So basically im trying to make a type of "dragon" / "flying" movement. If you are familiar with the game "School of dragons" im basically trying to replicate that. Where if you press space you go forward in whatever direction you are facing and if you press "w" with space you start to move up and if you press "s" you go down. Im gonna try to do some experimenting by myself later but i thought gathering some information from some actual smart people might benefit me.

So heres some ways im thinking. I dont think i can use the Horizontal or vertical inputs that built in with unity (maybe i can use vertical not sure) correct me if im wrong though.

so maybe i could use a rigidbody turn off the gravity and use add force? or use transform.position + "whatever way im going"

is one better than the other? what are the differences? is there another way i should go about it? Move position maybe? i thought maybe using an empty object putting it in front of the "player' and making it move up or down and then making the character look at it while moving forward so it just moves forward with the rotation direction if that makes sense? anything helps! thanks!