Equipment

For lacrosse, your need cleats, a cup, elbow pads, gloves, chest pads, a stick, and a helmet with a mouthguard.

Cleats

The best cleats for lacrosse are Nike cleats(In my opinion). They have a lot of brand deals and also have football cleats that you can use. They fit all range of sizes, and are all high quality.

Auckland Museum / CC BY (https://creativecommons.org/licenses/by/4.0)

The best elbow pads are Under Armour ones. They are very comfortable and cover a lot of skin, giving more protection.

Gloves

The best gloves are Nike gloves. with a variety of sizes colors, comforts, and grip, they are the best type of glove to buy.

Yarnalgo / CC BY (https://creativecommons.org/licenses/by/3.0)

Chest pads

For chest pads, there isn't a better brand, you could buy any brand and it would work, as long as it's comfortable and fits well, it will work.

Willyp15 / CC BY-SA (https://creativecommons.org/licenses/by-sa/4.0)

helmet

Again, there isn't a specific brand to buy, Cascade sells the most helmets, but brand doesn't really matter for this, only size, shape and fitting.

Billybenz4 / CC BY-SA (https://creativecommons.org/licenses/by-sa/4.0)

Stick

For a head, there isn't a specific brand, it depends on your playstyle, how quick you want your release to be, and how you want your pocket to be strung. The stringing on the stick will change the veloctiy and your shot. For a stick, it depends on your position. A defender uses a long stick to better defend. For a middy or attack player, you use a short stick for more control. The brand doesn't matter, but you still want to look for the best stick possible.

Pink_mesh_lax_head.jpg: koobert on Flickr (Yarnalgo for black background and crop)derivative work: Yarnalgo / CC BY-SA (https://creativecommons.org/licenses/by-sa/3.0)

This is a diagram of a lacrosse head

Tyler Reams / Public domain

That's all the equipment you need to play lacrosse.