Since no one else is answering I guess I'll try, though I'm really not qualified since I only just took N5.
Absolute first thing you need to learn is Hiragana and Katakana, you can't do anything else until you've got them down. You can memorise them all for recognition purposes in a day but if you wanted to learn to write it'll take slightly longer learning the stroke. I used white rabbit press cards and just went through them constantly until I could write both sylibaries from memory.
After you've memorised the Kana you have three main fields you need to learn simultaneously:
And two you should maybe wait a month until you've built up some vocab.
Some people don't bother to learn Kanji separately from vocab and that's fine; I can read a metric fuck ton of words I've learned that are written with Kanji that I haven't learned, but I wouldn't be able to write them down or recall them from memory, only recognise them, and I'd have trouble telling them apart from similar characters.
Other people use methods like RtK and Heisig, which use memory tricks and other arcane shit to remember Kanji quickly. I don't really know shit about this method as it doesn't interest me since I want to be fully literate and able to write, even though most people use keyboards nowadays, which brings me to:
The slow way. If you want to be fully literate and learn the stroke order, kunyomi and onyomi of every Kanji and be able to write them you can do it the slow and grinding way, which is what I dot. I'm sure everyone uses different resources etc. but I use a series of Kanji text books published by Bonjinsha, but the information in the books is available freely online, I just prefer not using a computer for everything except vocab and listening (and reading I guess). I use the textbooks and a giant stack of Japanese manuscript paper, with one piece of paper for each character I write out the character multiple times down an entire row and write the meaning and the readings hidden in the margin. I do roughly 4 new characters a day and revise every previous character (within a time limit, else I'd soon spend all day doing Kanji revision). I revise each Kanji by glimpsing the character, saying out loud the meanings and readings, then checking the margin, if I get it right I write down the character once, if I get it wrong I fill out the entire row while reciting the readings. Even though I use this method I can't really recommend it to you in good conscience, for 90% of people just learning to recognise Kanji and remember the readings will be fine. The only reason I use this method is because learning how to write makes reading handwriting and shitty fonts a lot easier, which will help with my imaginary future career as a translator.
I know you said you don't want to use a computer, but short of reading a dictionary I don't know what you could do without Anki, I've never met anyone that doesn't use it.
Install Anki, import Core2k/6k with sound, install Meiryo UI font, change the card font to Meiryo UI, turn off suspensions, turn off review limit. Don't be too worried if you have false starts with Anki either, it has a UI from hell. Oh and fiddle with the new cards per day option in the deck options, don't feel bad about lowering the default if it's, I only do 10 a day and I just aced the vocab section in N5, sometimes I turned new cards off all together for a few days if an annoying word group was clogging up my revisions. Always do your revisions, every day. This is the only method I know and I'm sure some people disagree with my Anki setup or whatever, so feel free to chime in if you've get any other ideas
Get Tae Kim, everyone I've talked to says it covers N5 and N4. After that I'm as clueless as you, though I plan to get Kanzen Master N3 Grammar and Dictionary of Intermediate Japanese Grammar once I pass N4 (or if I only fail it by a slim margin). Tae Kim is free online and has a paperback version as well.
I'm am REALLY not the guy to help you here.
Nor here really, though I feel I did okayish on the reading comp questions in N5(I read very slowly though). A lot of people recommend Yotsubato. I already "read" a lot of raw manga using capture2text and Rikaichan, but that's not me trying to learn Japanese it's just me wanting to know what happens next and not being able to wait for the real translators.
Oh yeah, install capture2text and learn how it works, also install Rikaichan/kin/sama depending on what browser you use. Hope I could help in someway but I only have my experiences to go on, hopefully someone more experienced can come along and give you some better advice.