First piece of advice is buy what you need, not what you can afford. As Magic said, avoid all API test kits, they have no place in this hobby. While reasonable for freshwater use, their marine range is worse than useless and
will cause grief.
I'll number them in order (based on my opinion) and give some recommendations, most of which are agreed as standard in this hobby. Note that those above the line, you really should have had prior to getting your tank wet.
1.
Refractometer designed to test sea water (not just salt water) in the minimum range of 1.000 to 1.050 specific gravity and with automatic temperature control (ACT). It needs to be properly calibrated so you'll need a calibration medium too. This measures the salinity (salt content) of your water - the most single important factor in success or failure of your tank. It is also useful when (not if) you need to treat for marine ich as the best treatment is hyposalinity and an accurate refractometer is critical to that process too.
2.
Reliable thermometer. Avoid anything that stays in the tank like hang on units as they all eventually break/fail and pollute the tank. *Note most PH pens have built in thermometer.
3. PH test kit, I prefer a PH pen (cheap on ebay) as they give you a digital reading, come with a digital thermometer and above all don't require you to decide what shade of colour your water is. if you buy a kit instead of a digital tester, avoid colour comparison types like API and at least buy a good titration kit where there is an obvious change of colour as opposed to guessing shades of colour.
PH pens also need to be calibrated from time to time but it's really easy.
ALL OF THESE YOU SHOULD HAVE ALREADY OR YOU ARE FLYING BLIND IN A CRIPPLED CRAFT.
4. Next you need to be able to monitor your cycle. You need a good ammonia test kit and nitrate test kit. I and many others recommend Salifert (titrate kits). Many will tell you you need to test for nitrites too but it's not really necessary and cycling is the only time you ever might want to test nitrites. At this point you NEED to understand the nitrate & bacteria cycle. If you don't, study it ASAP but essentially:
Ammonia (toxic) becomes nitrites (not as toxic), that in turn become nitrates which are non toxic but feed algae blooms etc. Some but not all nitrates will turn to gas and exit the aquarium. These are the small rising bubbles you will see in your tank once it is mature.
5. Tests for Calcium (Ca), Water Alkilinity/Hardness (dKH), Phosphates (PO4 or PO3). Without doubt, the ONLY reliable way to measure phosphates is with a lab grade test kit. Most use
Phosphate 'eggs' from Hanna Australia, they sell direct to hobbyists.
HI 713
Checker®HC Handheld Colorimeter - Phosphate Low Range
There is now some serious discussion that we should check for phosphorus rather than phosphates but that's an advanced chemistry discussion.
Salifert test kits for Ca & dKH do a good job. Some people are moving to Hanna checkers for this too but you can decide in a year or two.
Lastly (debatable) you will at some point want to check for magnesium as it effects PH among other things but you probably don't need that right now. Some also test for strontium, iodine, etc but these are minor trace elements at best and a good water change schedule is all you need to keep these right. In fact a good water change routine will keep may things for drifting out of whack.
THE GOLDEN RULE IS DO NOT ADD ANYTHING YOU ARE UNABLE TO TEST FOR which brings us right back to why you need ph pen, refractometer, etc, right now. :)