You definitely need a relay and typically it is controlled by a low voltage output from your alarm system. Simply connecting the alarm signal to an appropriate type of relay works (the ways they work vary by manufacturer and setting, it should be laid out in the documentation for the alarm-connected device- so you need to give us more information)
Opto isolation is good to have if there is a chance of lightning hitting nearby trees. In a world of long wires and lightning, given how cheap a relay board with opto protection is now, why not, it should be opto-protected.
I have an alarm - a real alarm system.. so at the time it was being installed, I used a very sensitive relay board from Elk specifically for alarms, which was kind of expensive but I now realize that a great many other relay boards would have worked just as well and have been much cheaper (and they also provide opto-isolation from high voltages going in either direction- useful if there is an almost direct lightning hit.)
As far as flood lights you only need to get a generic light that shines in two directions. An adjustable light with two separate floodlights. Typically they mount to a wall in the middle and can shine both ways.
Watch out for false alarms- be considerate of others sleep.
If it would bother neighbors, better for your light to only go on if somebody is right there than go off every time deer walk by, etc.