I would start by reading the general history of the period by an acclaimed historian, could be Niel Price or Else Roesdahl.
Then I would read a retelling of the myths. It could be Norse Mythology by Niel Gaiman.
After that I would read a book about norse religion. A classic would be Myth and Religion of the North: The Religion of Ancient Scandinavia by Turville-Petra, but that is hard to get hold on. It could also be something like Scandinavian Mythology by Hilda Ellis Davidson.
Then I would read the sources.
The Elder Edda/The Poetic Edda (two names for the same work) is a collection of poems, most of them date back to heathen time. The Havamal many talk about is part of this collection. Read a modern translation of the complete set of poems. Could be the one by Carolyne Larrington, Jackson Crawford or Andy Ochard. Its always good to have several translations at hand to compare, when I doubt. Don’t read the 100 year old translations from the net as your first choice or all those “study Havamals” from internet shops.
Be a little more cautious with the younger Edda. It’s the Christian Snorri Sturlassons interpretation of the poems of The Poetic Edda. Its an important source, but has to be used with care. Read also a modern translation. I would suggest the one by Anthony Faulkes. That book can actually be found for free online
Its also good to read The Sagas of the Icelandars, The Heroic Sagas, Saxo and Snorris Heimskringla. As always read the modern translations if possible. The elder translations are usally is a hard to read language and has sometimes been altered to fit the morality of the time of the translation.
Then I would go on to other books, because I now have a good broad understanding of the history and myths. A lot of books about Germanic/norse and the runes religion by modern practiceners have a lot of modern ideas an ideology. That is what is to be expected. If you have a broad understanding before reading those, you can see what is what.
Some of the Elder stuff can be bought fairly cheaply from used bookstores, like Abebooks or the Amazon sellers. It is also a good idea to use inter-library loans if your local library doesn’t have the books.