Test kits you want, look for aquarium shops and places like that.
You want a test kit that can do the following tests for fresh water
pH (some kits will have a single wide range pH and others will have a pH that does 6-7.6 and a high range that does 7.4-8.8?)
Those are the most important tests for cycling up and a water thermometer might be a good idea too.
Other tests might be nice but are not normally required for hobby scale aquaponics.
For gravel. Arm yourself with some vinegar and some water and a clear container so you can fizz test your options. You can go to landscape supply places that might have river rock or lava rock or find an aggregate supplier if you have a truck to haul your gravel. You will want to get a hand full of your possible gravel and rinse it with the water then put it in your clear container with the vinegar. If it just sits there doing nothing in the vinegar you will probably be fine with it.
If it Fizzes like alka seltzer DON'T buy it. If it bubbles just a tiny bit it may be ok (though it might be worth a second rinse and then dropping into vinegar again to see if perhaps the small amount of bubbles were just some dust stuck to the rocks) and keep in mind very porous stuff like lava rock may bubble a bit just because there is trapped air in all the little nooks. Most aggregate supply places are likely to have lots of limestone on site and dust from that will fizz so washing is important to avoid false readings or extended elevated pH during cycle up.
Note about expanded shale and slate. It will have an initially high pH because of the dust from the kiln process and the fizz test on that media will produce fizzing. I might recommend an acidic rinse when you wash your expanded media before putting it into service in a system if you don't want to deal with an elevated pH through cycle up of that system. This need not be a strongly acidic rinse, I only adjusted the water down to about 6 when I did a test on some of the stuff.
If you are willing to pay the price for it, I hear it is really lovely to work with. I've never sprung for the expanded clay myself since it is normally really costly here and I can get a cubic yard of gravel for between $50-90 depending on what I get and from where and if they deliver or not. I normally buy media starting in quantities of about 3 yards.
Now some people will use a heavy gravel for the lower half of their grow bed and then fill the top up with expanded clay