"Съесть" means to eat all of something. Я хочу съесть это яблоко - I want to eat this apple. "Поесть", although it's also a perfective verb, doesn't have the meaning of finishing your meal. It rather means "to have something to eat", "to eat a little". So it should be followed by the Genitive form поесть (чего?) - супа, хлеба, каши etc. The Ginitive here is used to express the meaning "some of". If you don't say what exactly you want to eat then the correct way would be "Я хочу чего-нибудь поесть", but in informal speech people often use the Accusative case instead of Genitive - "Я хочу что-нибудь поесть". Actually your first variant ( Я хочу что-нибудь съесть) doesn't sound bad either. I could say that in an informal situation, especially if I wanted to emphasise I'm really hungry (so I will likely eat all of my meal). You can say "у меня" or "у вас" to indicate your or the other person's place. You can also add "дОма". "Можно поесть у меня (дома)". "Мы можем поесть у меня (дома)". - We can eat at my place.

"кое-что" and "что-нибудь" mean "something"..but you should say я хочу съесть что-нибудь что-нибудь is used to tell about thing that you know exactly,for example you want to eat,but in your fridge you have apple pizza and cheese and you didn't decide what to eat and кое-что is used to show that you know what you want to eat but it's like a secret.for example when you are going to eat a peace of cake but you know that your friend want cake too but he is on diet for example..so you hint at cake.. but the phrase я хочу поесть кое-что doesn't use..someone can say хочу поесть or пойду кое-что съем(if you know what to eat but don't want to name this product)

Разный смысл. Я хочу съесть что-нибудь ! - Смысл - не важно что Я хочу поесть кое-что ! - Смысл - известно что, но это секрет или об этом скажем позже :)

Correctly to use the first variant: Я хочу съесть что-нибудь.

А можно и так: "Я хочу ЧЕГО-НИБУДЬ поесть", it also means "I want something to eat", but sounds more natural to me...