I'd say just be sure to acclimate them slowly, add tank water to their water in the bag, take some water out - tank water in, take some water out. You'll dilute the LFS water until hopefully there isn't much left (maybe 10-15 minutes between each addition of tank water). You won't want to net them out of the bag, but (now that the water in the bag is mostly your tank water) pour them into the tank. This avoids them puffing with air, and no puffing means they didn't get stressed enough to puff (at least that's how I think of it.)
The brackish stuff will have to be from others - I know nothing about it, except you do it slowly. Too much salinity too fast can crash your tank. I'm sure with as paranoid as you are, you'll be careful. (One blessing of paranoia! You are extra careful, extra watchful, and do things with extra care.)
As for names, my personal suggestion would be to wait and name them based on their personalities. See what you call them, refer to them, or what they remind you of

My pets (present and past) all had cute names, but in the end the ones that stuck were personality references or attitude references. (My prissy cat was a whole mess of names - a year later "Miss Kitty" stuck. My Fahaka - I named it Tad (looked like a tadpole), Mud (Mottled and muddy looking), but after seeing how he tears things up like a pitbull - it's Vicious. It's quite fitting. Also, I liked the name because it was unisex, as you can't sex a Fahaka until it lays eggs... so I may never know if it's male.)
First meal, if you by chance can get a hold of a couple of snails from your LFS (rams horn, apple, tiny ones without a cone shaped shell) Toss a couple of those into your tank. My fahaka wouldn't eat until I introduced a live worm (from the bait store). He liked the action and the fight. You might try some bloodworms (If frozen, thaw first so it sinks. Avoid them feeding at the surface as it may cause them to 'eat' some air causing issues.) Some people use tongs or chopsticks to make sure everyone gets their fair share, but your babies might be skiddish of that, being a new tank and all. Don't be surprised if your babies don't eat for the first few days either - they may be pretty unsure about their surroundings. It depends on the fish though, I know some people's puffers were gobbling up food right away.
Tips:
Watch for sunken bellies and pearl poop. Could be signs of IP.
Watch your tank temp, I don't know if you have A/C at home, or if it gets hot in your house - I know that was an unforseen issue at my house. (baggies of ice in an emergency to save the day, but been able to handle it so far without...)
And be careful about feeding. It's hard to NOT overfeed them. Rounded bellies are good, but they may still beg for food anytime you get anywhere within eyesight. For my puffer it kills me to skip one day a week. Especially when my daughter is begging too... "Mooom, can I feed the puffer??" ... "Not today honey..."
All in all, I'm sure you will do just fine. You'll quickly get to know all of them and their personalities, and as long as you keep an eye on the water - well, happy water = happy fish. Happy fish = happy mom.
Congrats fluffypechey! I'm sure you will give them a wonderful homecoming, (just don't feed them cake!)
