Good idea on learning new languages! German is my native language, I'm (pretty much) fluent in English, and I speak/understand French and Japanese on a basic level. While I did a lot of studying for Japanese on my own, all the other languages I pretty much learned at school.
I can show you my road map for my past experiences with learning Japanese, but I can tell you that you have to invest a loooooot of time to be conversational level in Japanese and just for vacation there's only two things that make sense: First, learn Katakana and get good at interpreting them. It's only like 50 syllables, but they will be a great help on a vacation, especially in super markets for example. But even after learning them, you have to practice them and read 200-300 examples to get a feel for them. The good thing is: Japanese people use them mainly to "fake" the English language. For example: Terebi. If you know that R gets pronounced as L and B more like W, you can get closer: Telewi. Television. TV. You know probably see where I'm coming from when I say you need practice. But with just 3 syllables you know and you're able to read TV. In the super market, many of the bags say Miruku. What could that be? Us are often silent, Rs are Ls. Let's try it again: Milk. Ahh, you're currently shopping for milk! You can get a grasp of those Katakana pretty quick, because there are only like 55, and in today's age with the globalization and the internet, often times the Katakana will give you a context. So you will know a loooooot of words (check this for example: http://infohost.nmt.edu/~armiller/japanese/kanaloanfr.htm ). Of course they're not always used, but for me the Katakana were more than often a life-saver for context and are very little effort to learn.
My second suggestion would be, that you get a travel translation book with English and Japanese next to each other, where you can point to phrases for conversations in Japanese. With those little helpers, you're prepared for almost any emergency situation. You will be able to talk about/ask for directions, order the proper food in a restaurant, find bath rooms, and will be able to communicate with a doctor about almost any body part. Yet it's lightweight and easy to carry around. Very, very handy. I didn't really need it myself, but I felt safer having one with me, just in case.
If you're still convinced you want to go the full route, I'd suggest that you start with both Kana alphabets, which will already keep you busy for a while, you absolutely have to be fluent in them and be able to read them without thinking. Then you should grab a book (similar to Tae Kim's website for example), that will teach you the basics of Japanese grammar. When I was at that point, I started visiting weekly japanese classes for three semesters, which helped quite a bit to remember the stuff still (because I have context and associations with the grammar/lessons). After like 2 semesters of weekly lessons, we were at the point of learning the end boss: The Kanji. Those little bastards make the difference between people who do Japanese for fun and people who are serious about it. And there's no recipe for them. Some learn them faster in class room environments, some learn them faster by locking themselves up in a room for months and do nothing else. Some use spaced repetition systems (I know Anki (for offline learning) as a software for example). Some use context based spaced repetition where they try to trick their brain into associating something with it (for example Wanikani). For everyone there's a different approach and there's not general recipe for everyone, but one thing all have in common: it's a very looooong and very hard way which requires a fuckton of discipline (unless you're gifted of course). I'm not saying it's impossible, it's obviously not, but you pretty much need to dedicate your life (like 2-3 hours a day) to Kanji for months. And the even harder part: if you don't use them regularly after your vacation, they'll be gone faster than you know it. And be honest, how much would you be able to keep them in your brain afterwards? Katakana + translation script will be a couple of weeks of practice and in my opinion are perfect for a vacation. You're prepared, but obviously not conversational. But if you put alllll that work into Japanese and after a couple of months after the vacation you start forgetting all of it, that will be a lot of wasted money and time (and blood and sweat and tears).
I'm not trying to deter you from speaking another language, it's awesome, I'm writing in English right now, but I want to give you a realistic outlook on learning Japanese, especially "just" for a vacation. If you're still motivated and think you can do it, grab tables and Anki/Wanikani/any other spaced repetition websites and start learning the Kana. Once you're done with them, I can tell you already that Kanji are a hundredfold the work of the Kana, if not more. Needless to say, I never learned more than 200-300 Kanji at which point I could not put more time into my Japanese and without time and dedication, it's near to impossible. I was at peace with myself, knowing that this feat is just one that's too big for me. I was happy to know the basics of a beautiful language and I love visiting the country, but I found in the end I get happier when I put my time into other things, and so I bought a piano (which is getting dusty now goddammit).
Good luck with whatever choice you make, I hope it's the right one for you and an update in half a year would be interesting :)