我买了一期新的我最喜欢的体育杂志就赶紧回家，急着想读之自娱。(amuse) 

I bought the latest issue of my favourite sprots magazine and rushed home, for I couldn't wait to amuse myself with it. 

As soon as I bought the latest issue of my favourite sports magazine, I went home to amuse myself with it. 

I went home immediately after I bought the latest issue of my favourite sports magazine, because I was eager to amuse myself with it. 

amuse意为使。。。愉悦、使用。。。快乐。宾语为某人。自娱应为amuse myself with sth.急着想自娱，意味着还没有发生，故用不定式表示。汉语“读”不必翻译。杂志的一期英语是issue.

赶紧回家，意味着着买和回家两个动词衔接很紧，可用动词 and rushed home. 也可以用as soon as或immediately after表示二个动词的紧密衔接。急着回家阅读是赶紧回家的动机，于是可用并列连词for,或者because从句。也可以用不定式表示目的。

总之，只要把握了其中的逻辑关系，amuse myself with sth. 表达的方式可以有很多的。