The truth about Alfred?? You're not going to get it from The Last Kingdom because it's the first in a series - so the Alfred you see in that book is young, unformed and a long way from his greatness - you will have to read the rest of the series to see how he develops. But nothing important in the book was 'made up'. The scene where he laments his youthful sins comes from a contemporary document (Asser's Life of Alfred). He's a great man, and a good one, but also complicated. It's not certain that he had an illegitimate child, but very probable (there's some documentary evidence, not, perhaps, enough to be definite, but suggestive).
I suppose he is called 'the Great' because, more than any other man, he is responsible for the survival of Saxon culture in what we call England. Without Alfred there would not be an England. He is a man with a vision, and a mission. His vision was of a Christian country, suffused with learning, ruled honestly, governed by fair laws. That, by itself, makes him unusual and great. But he was doomed to fight a war against the Danes and it's a war he wins. I suspect he was not a natural warrior. He's too sick all his life, he's a natural scholar, he's very pious - but he's forced to fight for his country's survival, and he fights the war with the application of his superior intelligence. I've no doubt he was a very, very clever man, and his method of conducting war is, essentially, intellectual. And it worked. He alone is responsible for the survival of Wessex. the rest of what would be called England is under the rule of the Danes, but Alfred ensures that there is a solid, strong Anglo-Saxon kingdom in the south and, in his lifetime, he extends his rule over much of what is now the Midlands. His son, his daughter and his grandson complete the reconquest of England, and it is his grandson, Athelstan, who is the first king of England. Without Alfred we would probably be speaking Danish!
Your best source is a book (recently published) called Alfred the Great, The Man Who Made England, by Justin Pollard. It's a life of Alfred and it is well done. You'll get more or less everything you need to know from it. It was published last year by John Murray and may be in paperback by now.
My Alfred is deliberately less than heroic. I find him horribly pious (which I'm not) so I have fun with that - but as the novel series progresses you would detect a growing and grudging admiration for Alfred's cleverness. I think he was a great king, but not one you'd want to share a pint with!
Good luck with the project - and thanks for writing!