你的断句有问题。这里的 did was rent 并非你想象的“连用”。你的句子结构如下：
So the first thing (主语) we did (定语从句) was (主句谓语动词) rent (不定式作表语，省略了to) a fantastically expensive sixth-floor apartment the size of a cupboard.
根据英语语法，当主句含有动词 do（包括它的其他形式）时，谓语系动词 be 后面跟的不定式可以（不是必须）省略 to。即原句等于：

So the first thing we did was (to) rent a fantastically expensive sixth-floor apartment the size of a cupboard.

又如：

The only thing I can do is (to) apologize. 我能做的唯一一件事就是道歉。
What he does is (to) teach. 他的工作就是教书。
What you do is (to) mix the eggs with flour 你要做的事是把面粉和鸡蛋搅和在一起。
All I did was (to) press this button. 我所做的只是按这个电钮。