I would recommend Joakim Anderson's Lagom Guide To Swedish, it's friendly to beginners but will keep being helpful later as you learn.
Disclaimer: I haven't started learning yet, but I have bought "Colloquial Icelandic" after browsing it and it seems to be really well done. There is a kindle version so you can browse the first chapter to see if it would suit you
https://www.amazon.com/Handbook-Finnish-Jukka-K-Korpela-ebook/dp/B015AM7Q90 is excellent (it's almost bizarrely thorough).
https://smile.amazon.com/gp/product/B081N3GWCH/ref=ppx_yo_dt_b_d_asin_title_o01?ie=UTF8&psc=1 This book is only $7 for Kindle! I've enjoyed it so far. I'm 4 chapters into the first short story.
I would recommend a book that explains grammar first and foremost. Vocabulary is key for developing your language skills but it comes later, you have to lay the ground work first. Try something like this book on grammar. I had a look through it and it looks like it's quite good at explaining and is what I would have given myself if I could go back in time to my beginner self.
I started with a textbook called Rivstart, but I wouldn't recommend it for a complete beginner for two reasons: firstly it's all in Swedish so without a teacher, it's quite hard to get into, and secondly, it doesn't explain how the language works. Things like word order and endings are really important in Swedish, in a way that they're not in English, so I would really recommend a grammar book, like the one I linked above.
I'd also recommend this youtube channel. The host speaks very slow and clear Swedish so you can hear each word and hear the tonalities of the language, which you can't get from a textbook. The videos also have Swedish and English subtitles so you can follow along.
Good luck with your language journey! Swedish is a beautiful language and I've loved learning it! Lucka till!
This might be easier than you´re asking for, but I heard about this other book: "Árstíðir: Sögur á einföldu máli" that is aimed at Icelandic learners.
I've been using this one. It's not perfect, but it is adequate and makes reading Swedish books on Kindle a much more accessible experience.