Hi Richard,
Welcome to Melnet- It sounds like you are in the same place I was in a year ago- just started with a 1 row 1040. As you have a 1040/D you also have the "classic" pitching for Irish and modern English 1 row. Perhaps you did more research than I did-as I chose "G".
Your profile doesn't give any location- though "Shepherds Hey" suggests you are in England and presumably looking for starter tunes that belong to English tradition.
My first tune on the melodeon was " Merrily we roll along" , followed by "Johnny Todd" - a traditional song from Liverpool which I learnt fifty years ago in primary school- and became on the melodeon, the first tune I ever learnt to play by ear (on any instrument) and then: Twinkle Twinkle Little Star, Amazing Grace, Auld Lang Syne and then into Gaidhlig music with "Loch Liobhan" . Nursery rhymes are really good starter tunes for the one row and David Mallinsons tutor is particularly good in this respect.
Do not under rate the songs you learnt in childhood- as tunes to be worked out from ear and played and enjoyed as well as being a basic repertoire to build on. Their simple rythms also give you something clear to start working on a rythmic bass- if that suits your personal style. As you are starting with the 1 row I would say avoid Ed R ennie's book - his introductory method is very focussed on 2 row D/G. It is just confusing a a starter for the 1 row.
Hope this helps and enjoy the learning experience