"Vamos" is the correct one "Estamos yendo" is the present continuous form. You are doing the thing right now. -Estamos yendo a casa. -We are going home. (meaning you are on your way) If you want to use "we are going to" as a future using "vamos" or simply the future tense is the correct way: -Vamos a necesitar una mesa para tres. -Necesitaremos una mesa para tres. Both mean: We're going to need a table for three. I hope this makes sense.

Hoola Chris! Mira, si estas en Colombia por ejemplo y vas a salir con amigos o familia a comer o beber algo, podrías usar la segunda frase " vamos a necesitar una mesa para tres". La palabra yendo hace parte del verbo ir y en este contexto no aplicaría.

I agree that "vamos a necesitar" is the better option. The other one seems like a literal English-Spanish translation. I don't believe I have ever heard a native speaker use it, but I wouldn't be surprised if it were used by speakers who are very much in contact with English. That is not an insult. Language transfer is inevitable when two or more languages are in contact.