Looking for the most common 12 GA, semi, that you can shorten with a light and possible laser mount on rail? What are the tiers? Budget, average, expensive?

https://www.atlanticfirearms.com/taxons/ak-47-shotguns

590 Shockwave with brace.  Replace forend with Magpul and add light.  Add OPSol miniclip for 8+1 capacity with minishells.

It's not common, but the Tavor TS12 is pretty short and interesting.

I think this is what you're asking:

Remington 1187 Police - bottom end but reliable, just keep some extra o-rings for the gas system on hand and change them every 500 rounds or so. Starts at about $600

FN SLP-1 - last time I saw one it was about $1000

Benelli - choose your poison, M2 Tactical, M3, M4 - M2 start at about $950 and go up to about $1400 depending on the shop, M3s aren't available very often and fetch about $1500 NIB, M4s are $1400-1700 depending on the shop.

Beretta 1301 - last one of these I saw in a shop was right at $1000

All are factory 18"ish barrel guns. Price anywhere from $600-1700 with the Remington being on the low end and also the heaviest. Either the Remington or the FN will be the softest shooting. Benelli M2 is the lightest, M3 is convertible semi/pump but doesn't work like it sounds and doesn't have screw in chokes, M4 is the top end price wise and the heaviest Benelli, but I would put an M2 up against it on reliability any day. The Beretta 1301 is somewhere in the middle.

My suggestion (if you just have to have a "tactical" gun, is get a Benelli M2 (model # 11054) - get the 18" one with the "rifle sights", not the ghost rings. (Although they are more common with the GR sights) Get a Nordic magazine tube extension and one of their barrel clamps with a rail on it if you absolutely have to have a light. Find a light weight, thumb activated light like a Streetlight TLR-1, skip the laser and be done with it. If you shop around, you could be in the whole thing for about $1200 and it will last forever. Don't spend any money on any aftermarket parts except the magazine extension. No side saddle shell carriers, etc. You can reduce the reliability of a Benelli M2 by hanging a bunch of extra weight on it, and you will find that after time you would rather have a light, easy to maneuver gun.

If you don't mind the extra length and can live with a raised rib barrel and standard shotgun beads, the Benelli M2 21" field gun is really light and handy. Plus, the comfortech stock really works as advertised and soaks up some recoil. These are super versatile and I had no problem making 100 yard slug shots on IPSC targets out to 100 yds with just a bead on the rib. The 21" also makes a damn fine light weight quail gun. I sold mine a few years ago and have come to regret it. There's a reason why most 3-gun competitors don't use ghost ring sights. They're slower and just aren't a necessity on a HD shotgun.

Something else to think about in an HD shotgun - the shorter the magazine, the lower the capacity. Since you're talking semi autos, stay away from the Remington Tac 13. It's a neat novelty, but not practical and low capacity. You don't want to try to reload it under pressure. I mentioned 3-gun above and it's really become a reloading competition. Whoever is the fastest on the shotgun will usually win the stage and in most cases the match.

They have not been made in a few years, but the Beretta 1201 might fit your bill if you are on a budget.

That  is my go to HD shotgun.

Mossberg 930SPX

M1 Super 90 Benelli.

930

I had a suggestion until I read the underlined. I was going to say Benelli M4 is the standard.
https://www.benelliusa.com/shotguns/m4-tactical-shotguns

Hands down my M1S90 PoPo tradein is one of my favorite guns.  Ghostring sites, Surefire foreend and semi auto, how can you go wrong?

930 JM Pro

when you say shorten, do you mean to below 18" and into NFA area? if not, most of the guns mentioned come available with 18" barrels. I have a winchester SX2 (FN SLP are identical) and it was great. ran even with garbage loads, soft and accurate. Wouldn't hesitate to get one again or the FN.

That said I am shopping for a benelli. Why? No idea. Don't own one, never shot an M4, always wanted one, that kind of thing...

I use an NFA 870 for HD. Barrel is down to ~12" and it has the magpul rail and a light, so it's handy. I need a new barrel since I had rifle sights that broke off, but it's all the size advantages of a shockwave with the stock advantage of a stock. The stamp was cheaper than some of the braces. Still longer/heavier/lower capacity than a short AR, so take that for what it's worth.