"We should be friends" can be translated as "我们交个朋友吧。" And "Let's be friends" can be translated as "让我们做朋友吧。" Either of them is the same.:) Hope you make more and more friends.

We should be friends: 我们应该成为朋友。 Let's be friends: 我们交个朋友吧！ The second one would be more natural to say in Mandarin, although, normally, I don't think Chinese people would literally say it out. If we want to make friends with someone, you just do whatever it takes to be friends. You don't necessary to express it verbally.

咱们做朋友吧 = zán-men zuò péng-you ba

我们应该可以成为朋友！ （让）我们做朋友吧！

我们交个朋友呀？