Hi, I have done 90% of my diving in Cyprus so I may be able to point you in a few directions. Generally the water temperature will be around 19 surface and 17 at depth and the vis is likely to be 15m - 30m.
I am not familiar with any diving shops in Limassol myself, but I know other people who have used them. There are a number of good dive sites off the Limmasol coast so you won't be disappointed.
Limmasol is lucky to be close to one of the best wrecks in the world, the
Zenobia at Larnaca. Most the wreck is deeper than 18 meters but I know OW divers get to see enough to make it a worthwhile trip (although I have never done it myself). I'll eat my dive boots if there isn't somewhere in Limassol that will run a trip there at least once a week.
As you have a car, you may like to make the 45 minute trip to Paphos and take some dives there. I would recommend
Cydive near the harbour - I'm yet to met a nicer bunch of people, although maybe I'm biased as they got me through my OW last year

They run a 14 day rotation on the dive sites and are open 7 days so you could have 28 dives to choose from. The sites are pretty varied, with shore dives, wrecks and other stuff.
I'll be out there myself during April so who knows, maybe I'll be buddied up with you or your partner! Hope this helps.