Arduino Mega / Servo / Linear Drive programming

We are developing a machine and are looking for person with expertise in Arduino Mega, Touch Screen, Mitsubishi Servo Driver.

We will be using the following:
Mitsubishi MR-J5W3-222G (Servo Driver)
Arduino Mega 2560 R3
ER-TFTMO90-2 (9 Inch Touch Screen)
MELEXIS US2881 (Hall Sensor)
Servo Motor (12Nm) - 1 No
Linear Motor - 2 Nos

We are looking to create animated transition effects for buttons. You can suggest the best suitable programming option for the same.

I have attached the basic requirements in word document.