j'ai choisi un roman court et j'avais mon dictionnaire

James, 

The use of both passé composé and imparfait in the one sentence is not at all unusual. See this lesson :

Using the compound tense (Le Passé Composé) on its own or with the imperfect tense (L'Imparfait)

The choice of a book is a single, defined, brief event. It is also the main focus point of the sentence for the speaker (David) - passé composé is appropriate. 

Having the dictionary is ‘background information’, he likely had it before ‘making the choice’, and used it after making the choice, but how long he had it for is unspecified, and he has it if he needs it, not as his main focus. Also, having the dictionary lasted longer than ‘choosing’, and this is relevant when describing ‘actions’ that overlap - all of these factors lead the French speaker to use imparfait in this context. 

I think it is essential to go beyond the ‘rules’ of the tenses and move on to understanding their application, and more importantly the meaning the different tense conveys. There are many good overviews but I found the link below one of the best for further developing a feel for the different uses of imparfait and passé composé - you will find what I have mentioned above is well covered in the text and accompanying short video scenes. 

 https://www.frenchtoday.com/blog/french-verb-conjugation/passe-compose-versus-imparfait/ 

Additionally, if you want to listen to some understandable French covering these areas well, this YouTube by Hugo Cotton is excellent. (subtitles available)

https://youtu.be/3rpQ5xeFneg