Top of the list for meteorite hunting equipment is your eyes. So the first thing to do is to tune up your eyes for what meteorites look like. After you are a little familiar with how rocks from space look you can gather together some other essential equipment and some other helpful stuff too to that you might want.
Most meteorites have some nickel iron in them. Most but not all will stick to a magnet. Many but again not all can be located with a metal detector. Some are on the top of the soil and have so little iron that your eyes and a magnet glued to a stick are all that you really need. But to do the job right here are some other things to take.
You will want to record the location of the find. So a GPS better than the one in your cellphone is needed. Though they will work in a pinch they are only accurate to about 100 feet.
Carry a camera to take pictures of the find site for your own records and to document it officially if you choose. You can also take a picture with the GPS in the frame so that you know what piece was found where without a lot of time lost in the field writing notes.
If you are hunting with a metal detector you will need something to dig up the targets that it responds to. So a pick or folding shovel or certainly at least a sturdy garden spade need to be with you. Remember you have to carry all this around for hours in your back pack so weight may be something to think about. You can attach a magnet to the pick or spade too so that as you dig the target will stick. That saves some time.
The backpack I mentioned so add it to the list. It should be large enough to hold the snacks and food and drinks that go with you. Liquids are essential even though they are not equipment. It is great if the back pack has a lot of small pouches with zippers. You will need places to put some of the other items that are good to have.
A diamond file to grind a spot off a suspect rock to see if it is meteorite like inside, a loupe to examine up close the rocks that might be meteorites. Baggies and a marker pen to hold and identify the specimens you find.
I like to have a digital scale and a toothbrush and artist brush to weigh and lightly clean specimens back at camp. I do nothing harsh and never liquids on the stones just brush off the dirt and dust.
Well that will get you going; you will add things as you get experience, have fun and good luck.