You need:
- kits that say they work on saltwater (ok if they work on fresh too, just not fresh-only)
- liquid kits, not strips. Strips are so unreliable and easy to contaminate that it's not worth it.
- hydrometer or refractometer, auto-temperature correcting refractometers being best, to measure specific gravity
Sw absolute minimum for liquid kits: high range pH, ammonia, nitrite, nitrate. Things you should have eventually when you are looking at animals: KH, phosphate, and calcium. If up-front cost is an issue, get the basic ones now and then get the other ones when you go beyond hermits and snails. KH and phosphate in particular are very important for debugging common problems like pH swings and algal blooms. Calcium is just a good thing to keep an eye on over time since it can also affect pH. Other things beyond that tend to be on an as-needed basis.
It's up to you what kit brands to go for as long as they're liquid. Some people swear by the more expensive ones like Salifert, and some of those more expensive kits do offer increased precision for things like nitrate. But, I've never had use for that regularly, so I get what's cheapest while being a liquid kit. In my area, that means API kits, but I don't know what options you have in your region. I've never had a need for more expensive brands except in two very special cases that you're incredibly unlikely to ever run into (specifically testing for trace things like Strontium and trying to debug rare cases of reagents interacting with a dye or something that an animal has released into the water).