Arduino with 24V DC & 220V AC

Using Arduino Project Guidance
1

I'm working on a control project using arduino , the components are:

inputs: proximity sensor 24V DC , Accelerometer and Gyroscope 5V DC
outputs: AC motor 220V AC , DCV 4/3 (solenoid) 24V DC

-I watched some tutorials recommending to use relay module for controlling the AC motor, Is that the best solution ?
The rated current for the motor is 13.5A and for the relay module is 10A so should I insert overload relay or something ?

-for the 24V devices, what's better to control them relay module, solid-state relay or transistor ?

-what's the size of the power supply needed for my operation as I have 5V and 24V? Can I use 5V battery or is it better to use to 2*12V ?

2

You better provide a lot more relevant information.

What is a 24V DC proximity sensor?

What is the rating of your 220 VAC motor?

What is the rating of your 24V DC solenoids?

What else - other than relays - would you use for controlling the AC motor?

Why would you use batteries?

What does this thing do?

3

You will need a contactor to control a motor current of 13.5A.
You could drive the contactor via the aforementioned relay.
Reason being, motors draw a LOT of current at startup ( sometimes 4 to 6 times full load) which will simply blow your piddling little relay to smithereens.
Control voltage for the contactor could be 24v BUT DC control contactors usually will cost a lot more.
Perhaps better to use 24V ac and provide a fairly hefty power supply maybe 4 amp.
Cost will be something for you to find out.