is those 300 kanjis enough for you to live there? or play games? I heard that you require around 1000 kanjis to read news papers.
P.S. How did you learn those 300 kanjis? tell me about first 80, did you use mnemonics? or books? what about vocabularies, did you use flash cards (the paper ones, not DS ones!)
Yes and no (though I probably recognize closer to 350-400 kanji). Japan is English friendly (for example - road signs are in Japanese in English so that most signs list either a town or official town building, like a town hall, in English and Japanese). That said I don't want to live like most of the foreigners here (especially the military people from the base in Misawa). I want to know Japanese, read like an adult, etc. So I need to know more, which is why most of my free time at school is spend learning kanji (kanjis sounds sub-standard to me - Japanese does not always plural and so words like samuraiS, etc., directly imported and then pluralized sound substandard in standard English).
As for games - depends on the game, like anything (books, manga, etc). I've made it through Dragon Quest Slime Mori Mori and Final Fantasy Tactics A2 pretty much just fine. But those games are meant to be easily accessible. I can get through Gyakuten Saiban because I know a lot of legal and mystery terms (from lessons in another Japanese book, the class I am taking now here in Aomori) and from my thesis research. This actually refers back to an earlier point - most stuff meant for older people (like adults) is less accessible, like xXxHolic.
You need 2,000 odd kanji to be a competent adult and to be able to read newspapers, etc. One of my exes was a self described kanji nerd (she took a class on Genji in the original old Japanese in high school and then Chinese in college) and so she knew 3,000+.
As for learning, I used the textbook you have right now to learn most of them. Use that. Seriously, you need a teacher (or a girlfriend - Kaoru and Rieko taught me a lot of kanji as I studied and they pointed even more out to me), but without one, that book is the best resource you have. I have said it many times before and I will say it again: that book is the single best intro Japanese textbook there is. USE IT. Right now I'm using PG O'Neil's "Essential Kanji," which is NOT a good first kanji book or reference book. But it's a list of 2,000 kanji in rough order of difficulty and usefulness, which is what I need; I want one big list to work through. It doesn't offer much in the way of mnemonics, and it uses an old list of kanji (toyo, versus the current joyo) so some of the harder kanji are not much help for me.
Use the book. Use flashcards to reinforce what you're studying. Then test yourself (Genki even has self tests in each lesson! It will give you a compound and ask either the pronunciation or the meaning or both).
What I do know is I go through O'Neil and write the kanji, the listed compounds, and readings over and over. Muscle memory is a good thing here, so kanji that I don't know or can't write off the top of my head I write over and over again until my hand knows what to write and the character looks reasonably good. Writing the compounds as you learn more kanji is good because the compounds will contain characters you are supposed to know so it is a good review. Just go through Genki and you learn a lot many kanji and (more importantly) a ton of radicals. When you've learned those (studying like you would for any other subject / any other class) start worrying about learning more kanji. The way people learn is different from person to person and Japanese isn't some magical subject. Learn it like you learned anything else in school.