I know this has already been answered but I will throw in my 2 cents also.
General starting gear needed to start sploring would by my mind be:
>Gloves (an absolute must)
>Dust mask or even better a workman's respirator
>Suitable clothing for the location, sturdy but inconspicuous.
>Good pair leather boots ( fabric will still get your feet soaked)
>A small reliable torch with an even light (e.g coast G50)
>Powerful head torch for lighting up rooms and allowing hands free movement/shooting
>A good backpack to keep everything in with a few different compartments,so you know what is where.
>A compact spare torch and extra batteries for your camera
>Freshly charged batteries in all devices including torches
>A bottle of water
>Snack
>Common f***ing sense/e.g no deaths by rusty wobbly ladders.
In the case of a camera, the best option is to buy the best DSLR you can within your budget , as you will get lots of enjoyment out of it even outside urbexing. However if you just enjoy the thrill of urbexing and taking a few record snaps, then there is nothing wrong with using a phone to do so.