The first one is a child's book - 'The Usborne First Thousand Words in Arabic' by Heather Amery and Stephen Cartwright. The slim volume is slightly bigger than A4 sized and consists of a series of double-page, full-colour pictorial spreads, each on a different theme e.g. the kitchen or the hospital. The main picture shows a large array of items in situ, whilst around the border there is a selection of the items which can be found in the main picture. These each have the relevant word written in Roman and Arabic scripts. At the back of the book is a dictionary with each of the words from the books written alongside the English equivalent. This seems to be a good book for me to leave lying around so I can keep dipping into it.
The second book is 'The Arabic Alphabet: How to Read and Write it' by Nicholas Awde and Putros Samano. This A5 sized slim volume has an introductory chapter on the language and then goes into detail about each letter and how to write the different versions of it. There don't seem to be any exercises in it, but the letters are laid out in such a way that I can easily copy them to practise my writing.
I read a lot of reviews of different books before choosing these two. They both had plenty of positive reviews and they seem to fit my needs at the moment. When I improve, and when I have more time, I'll look for a book which includes grammar and sentence structure and has exercises I can work on.