Yes, that SSR you've found looks suitable. If RS have a similar part that has zero-crossing switching, that would be better.
Zero-crossing switching means that the switch device will only turn ON or OFF at the instant that the AC mains sinewave crosses 0V, either upwards or downwards. This means that when the switching device turns ON, the load will see a voltage that starts from 0V and ramps up (the start of a cycle of the mains sinewave). Without zero-crossing switching, if the enable signal happens to occur when the mains sinewave is at a positive or negative peak, the load will see an immediate jump in instantaneous voltage, from 0V to the peak voltage (325V for a 230VAC mains supply).
So the zero-crossing switching feature reduces the worst case possible surge current in the load and is desirable.
The SSR that I suggested, and the one you have found, contain an LED, which illuminates a photodetector that drives the SCRs that switch the load. The LED is connected directly to the two "input" pins. So you need to drive the SSR as if it was an LED. This means that you need a current limiter of some kind; a resistor is the usual and simplest option.
The specification sheet for that SSR says that the LED has a maximum forward voltage of 1.4V at 20 mA and needs 8 mA to switch the SCRs ON reliably. I would run it at twice that current, i.e. about 16 mA.
If your Arduino is running at 5V, when the output is active you will have the following circuit:
Arduino output -------------/\/\/\/\/-------|>|--------0V
Excuse the ASCII art. That's supposed to be a resistor, and the LED inside the SSR.
There will be 5V (roughly) from the Arduino output to the 0V rail, and the LED will drop 1.4V, leaving 3.6V across the resistor. You want 16 mA (0.016 amps) to flow in the resistor, so use Ohm's Law to calculate R:
R = V / I
= 3.6 / 0.016
= 225 ohms
Closest preferred value = 220 ohms.
You could use a triac. Or you could use a bridge rectifier and an SCR. But in both cases you need electrical isolation between your Arduino and the switching device. It's a lot simpler to use one of these SSRs; these have a triac or two SCRs in them anyway, and are more compact and simpler to use.