Basically, it seems as though you are endeavouring to use your experience with firearms in the military with shotguns on moving targets. There are, of course similarities but the discipline is totally different. Don't go down the route of getting a shotgun that looks like a rifle. It simply won't be as good at clays. Shooting shotguns is much less about aiming and more about muscle memory and peripheral vision. You need a gun that is suited to the job and suited to you. One that you can swing onto a target and follow through. One that is easier to judge lead, so sights become nearly immaterial. There's a reason that the vast majority of people who shoot clays use an over and under gun.
My advice would be to handle as many different over and under guns as you can. Put them to your shoulder and simulate moving across the sky tracking a clay pigeon. As Atlantoo says, a couple of try sessions at a clay ground can be very enlightening. My son was in the military and took up clay shooting (and some game shooting). Initially he would stand and try to align the barrels, the front sight and the clay together. Completely not realising that the target was moving and if he shot directly at it, the clay wouldn't be there when the shot arrived! What's more, he took a few seconds aligning up the shot and by the time he pulled the trigger, the clay was all but out of range anyway.
It's interesting to note that fighter pilots in WW2 were given shotguns and clay traps to practice shooting in front of a target rather than at it, initially an alien concept. Occasionally an ex-RAF shotgun comes up for sale.
The other advantage of an over and under is that it can be used for pretty much anything you might get into later, shotgun shooting-wise. So, clays, vermin control, wildfowling, game shooting, etc. They are, for most people their go-to shotgun. If you want to continue the type of shooting you might have done in the military, then you could consider becoming a member of a range and get a rifle. But that's a whole other story.
Don't be put off by people arguing over such things as licences/certificates. They might seem like pompous asses (and maybe some are) but they are for the most part endeavouring to be helpful.
