to limit the speed:
var max_speed : float = 300
func _process(delta):
#move paddle to mouse at max_speed:
var pos = move_toward($Paddle.position.x,get_global_mouse_position().x, delta * max_speed)
#limit the lef and right position of the paddle:
$Paddle.position.x = clamp(pos,50,600)
Another way is using a linear interpolation, the movement is smoother but decreases as the object reaches its target:
var speed : float = 2
func _process(delta):
$Paddle.position.x = $Paddle.position.linear_interpolate(get_global_mouse_position(),delta * speed).x
If I understood your question correctly, this should help.