It really depends on your level. The book and CD are great because they start training your ear immediately. After you're comfortable with understanding simple spoken Swedish, it's important to build your vocabulary quickly. If you're living in Sweden, that's no problem. If you're outside of Sweden you just need to rote memorize as many basic words/verbs as possible so that you have a working vocabulary. There's a YouTuber who made a series called "Speak Swedish, Stupid" which is surprisingly helpful for understanding certain points of grammar and gaining some obscure (but useful) vocabulary. YouTube videos where people are just speaking Swedish (regardless of the topic) are good because you can change the playback speed. There are lots of Swedish YouTube vlogs. Whether or not you enjoy the content, they're great learning tools: people interacting with and talking about specific topics in MODERN Swedish. Several even have subtitles. Clara Henry, Tova Helgesson, Therese Lindgren, Misslisibell, Jocke & Jonna, Thomas Sekelius, Felicia Bergström, etc... There are a lot. I know Clara Henry has English subtitles on most of her videos. If you can understand normally spoken Swedish, you've won more than half the battle. Then it's just committing words to memory so you can produce your own. (As for grammar, it doesn't really matter. Even Wikipedia has a pretty good section. www.thelocal.se isn't bad)

Just leaving a comment since, I am a Swedish native, so have no experience on materials, but a Mr. Zhang here on iTalki might have some good tips, being a language teacher and learning the language himself and quite fast too, I might add. If you want to practise the language itself or have any related questions, feel free to contact me. A lot of Swedes live in England and especially London; you might just be in luck :).