The sensors don't look easy to interface with. You might have a hard time getting an arduino to read the sensors without having to hack them apart. As an alternative might I suggest using something like this; https://howtomechatronics.com/tutorials/arduino/ultrasonic-sensor-hc-sr04/
They're cheap as chips on ebay.
Secondly, your LEDs take in AC110-220V power. You can supply this and control it with an arduino using relays. However then you are working with AC power which can be dangerous to novices so make sure you are clued up and plan out as best as you can.
An alternative is that the power brick on the LEDs is taking the AC and stepping it down to 12v and ~300mA. I might suggest that you power the LEDs directly, bypassing the AC power brick, and then controlling the power to the each LED set with a mosfet and 12V power supply. Something like this might point you in the right direction - http://www.hobbytronics.co.uk/arduino-tutorial9-power
This solution will of course require a DC power supply at 12V that can support the total current (mA) that your number of LEDs will require. However, I'd say this is much safer than switching AC.
A good place to start with Arduino is simply the Arduino Uno. It's the most robust, easiest to initially work with and there's a tonne of support and tutorials.