Pre-lockdown we used to eat in a Syrian/Lebanese place every week or two, and I have my favourite dishes. But my suggestion would be just to go for the set menu on your first visit to make ordering easy. It looks like a pretty good selection. Just be careful to remember what each dish is as it arrives. Write the names down if necessary. Then next time, keep your favourites, and swap out some of the dishes you were not so keen on with something new.
You may be asked if you want everything (at least all the non-sweet dishes) on the table at the same time. That is how the locals eat. We normally prefer to get the food in two traunches, leaving the meaty stuff and rice to the 2nd traunch (main course, if you like). That way you do not get food going cold.
As @suiko says, Musar is good with many things. But the Musar people would say it works better with classic European food than Middle-Eastern, and I think I tend to agree. The locals would drink arrak. But don’t let that put you off - take whatever you like and see how it goes. Personally I would normally prefer to drink aromatic white wine, from Alsace for example, or light reds that preferably have some spicy notes - nothing too fancy.