I agree that carbon steel is a good choice, especially if the brine is inhibited as it should be and if the temperature does not get too high. We have also had good luck with installation of sacrificial anodes in the carbon steel tank.
A better lining. I am thinking a multi layer resin system. This is going to take some skill in surface prep and getting the cure correct.
I would install CP also to protect against the inevitable minor holidays in the coating.
If the carbon steel tank is in service you have a couple of considerations if your looking for long service life at that both hot and cold temps.
Need to know more about the temperature swings and normal operating temp but Derakane 8084 formulated in a glass flake coating will offer a very durable lining. At 60 mils thick if will fill the profile and should not have any pinholes or holidays. The temp limit is 80C so a blend of 25% Derakane 441 would increase your HDT to an acceptable range.
Sandblast profile is key....need 3-4 mils. Can get that with med. black grit and at least 100 psi at the nozzle.
I don't do this work anymore but I can help you write a specification that will provide 20 yrs of service +-.