Everything is right expressions. 너와 나 or 나와 너 is very formal and standard. It can be used in both written and spoken Korean. Here in 너랑 나랑 or 나랑 너랑 랑 is the connecting suffix form which is preferably toward to friends especially boy/girl friends and more commonly used in spoken Korean nowadays than written. 너, 나랑 is like "You ~~~ with me." ex) 너, 나랑 드라이브 갈래? = You! Wanna drive with me? 너, 나랑 가자 = You are coming with me.

Actually we don't use 너 나랑 expression and rarely use 너랑 나랑. If you wanna use 너 나랑, you can use such as 너, 나랑 같이 영화보러 가지 않을래?. It depends. I will show you some expressions. 너와 나는 참 많이 닮았다. 너랑 나랑은 공통점이 없구나.