i'd go either a 1/0 or 2/0 circle, most panfish have small mouths, such as whiting(gulf kingfish), croaker, pinfish, piggy perch, small black drum, sandtrout, spadefish, etc.

2 oz weights usually hold well in moderate conditions. try 2 or 3 oz spider weights.

+1 on fresh dead shrimp, but get it off the bottom and throw it under a popping cork with a wire leader. I use an old plastic bottle with a wide mouth and a screw top to hold the shrimp so I can stay out in the surf, but keep the shrimp "fresh". You need one with a handle though. The ones I have are from old pool chemicals. I tie about a 1/4" diameter cotton rope around the handle and the other end around my ankle. I carry it out with me, but just let it float behind me while I'm fishing. About an 8ft rope is long enough. Walk back out to the first sandbar and cast into the gut. Or swim to the second sandbar and cast out from there. When the fish are there, you WILL catch them. Trout, smacks, reds, small sharks, sheepshead, ladyfish, rays, gafftops, and unfortunately hardheads too. you'd be wise to take some kind of hook remover with you.

Quick question about tying drop shots for saltwater:

Am I supposed to tie the hooks directly to the line/leader (like in freshwater bass fishing), or add a branching mini-leader with a swivel (as seen in stores)?

If I'm supposed to add a branching mini leader, I'm guessing it would be far easier to just buy some, but theyre so expensive at $1.16 per rig,

I rarely get to fish exclusively on an outing. Most of the time it is on the beach with the kids, and as such hard to maintain full attention on the lines and rods.
I use fishbites with great success as it is harder to steal than dead shrimp and can be used for several fish (did catch 5 whiting in a row on a 1/4" piece and 1/0 circle hook). My kids (5yo, 4yo and 2yo) still like to purchase dead shrimp and see the fish on the bait shops, so we usually get some anyway. 1 bag of fishbites strips can be cut in little squares and last a long time, ends up being cheaper than buying bait, and fish can't steal it. Get the orange shrimp flavor.

My rod is a 7' Med fast action and casts 1oz pyramid without trouble and then a larger surf rod that I can lob a 3oz spider with similar setup double drop 1/0 or 3/0. Still have caught 6" whiting on the 3/0 circles. As mentioned, circle hooks allow fish the set themselves. My son has a 5'6" and my daughter a 4'6" UL both are Shakespeare cheapie combos with crappy 1000 sized reels, but have fought even puppy blacks and big whiting when the drag is set right.

Neither have wire leaders, I use 4-5" of mono 20lb and a dropper loop for the hook, 10" below I attach the weight. The less swivels and connections the better it is as. The kids reels came spooled with I bet 8 or 10lb cheap mono, but are still going almost 3y later. Never been bitten off, but I don't fish for monsters with those rods.
I have migrated to bigger hooks, 3/0 circles, so I am not fighting smaller fish, and decent eating size ones will still be able to get the hook in their mouths. (This is with Fishbites).

Ahh, I just looked up what dropper loop rig is and it looks more "natural" than the regular dropshot because there is a small amount of line in between the hook and main line.

3/0 circles are already so small to me. How are you able fit an appreciable sized piece of bait on a 1/0? Or do you not need that much to attract bigger fish?

I will try using a drouble dropper loop next time i go. Thanks!

what are "bigger" fish for you? 12lb and a 7' rod may not be the ideal setup for your targeted species off the surf.

I dont necessarily target anything in particular as I have almost no surf experience. In the meantime, catfish and croakers will be enough to satisfy me. However, if a slot/bull red or something similar in size bites on, ill be happy to fight it. Heck, a small sand shark will make me take many pictures lol.

I recently upped my line to 20 lb.

1/0 with a dead shrimp has caught bull reds. You have to becareful to play it right and not bend the hook but 3x strong hooks will solve that. But that would be in a situation where you're aiming instead of "blind" casting and trying to draw them in.
I think you're asking about if the bait will put enough scent in the water to attract a fish from aways off and the short answer is probably not.
I think if you are going for a "bigger" fish with a large piece of bait you should go for a fish finder rig with a stinger hook with a nice big piece of cut bait or live fish.
I have used double drop rigs with a 5/0 and a large piece of cut piggy perch and caught 41 inch red. But i have missed plenty of bites because the fish couldnt fit everything in its mouth. And it would be fairly interesting to try and put stinger hooks on a double drop rig, it may become a tangled mess.
As per the dropshot v. Dropper loop. In my personal experience the drop shot is meant for finesse and sensitivity for setting the hook. Dropper loop is more for putting out scent and motion via wave action but is easily tangled and can "foul" its self more readily. If your looking for life like apperences a fish finder is better(especially if you fillet the bait and use a strip so it flaps and swims in the current) and less detectable especially because the fish can't feel the weight of the sinker once it takes.
So one is not better than the other just pro v cons depending on application. If im trying to cast a country mile better believe that I will be tying a fish finder(sometime not if throwing into the wind because it can foul too) or drop shot. In a boat where casting isn't an issue and I'm trying to put more blood in the water double drop is what I'm tying. At the pier targeting fincky fish near the bottom I'm doing a drop shot or freelineing with or without a split shot.

Agree with the comments by eramos. Bigger baits will draw bigger fish, but there are more smaller fish in general and by targeting the fewer you reduce your catch ratios . Reading the waves and structure will allow you to try and put bait were your odds are better at finding fish moving.
I am not an expert, but I have caught big fish on small hooks and baits and the other way around too, but most importantly seldom get skunked.
A 1 to 3/0 circle, 20lb mono and fresh dead bait or fishbites will get you enough action to be satisfied if you have half decent water and can place your hooks were the fish are, whether 1st, 2nd or 3rd gut

If you are running 12lb test, you can add a shock leader of about 20 t0 30 lbs then can cast heavier weights. I have gone down to as small as #6 circle hooks, just to catch something. #1 to #2/0 hooks are usually the most productive, and can still handle larger fish. All you need is a piece of dead shrimp or squid about the size of your thumb on the hook. With circles you need the point to be exposed to insure hookups. I see a lot of people over bait a hook and then wonder why they aren't hooking up to anything. All they are doing is feeding the fishies. Believe me, if there are fish around, they will find your presentation.

You have to think about this one, for every big fish there are probably 100 to 1,000 little fish swimming by pecking on your huge hook that you are missing hooking up on.

Squid or Octopus work really good on the piers in Galveston. I use two 4/0 circle hooks.