Japanese is my fifth language, so I'm no stranger to learning a language. Japanese is, however, the first language I'd learnt that had a different writing system from English. In French, Spanish, and German, it was just a matter of adding accents, cedillas, and umlauts when needed, and there were perhaps a few different letters, like ch, ll, and ñ in Spanish, but nothing wildly different from English.
Japanese does occasionally use Roman letters (called romaji), which all Japanese people do learn, although it's mostly used for typing on a computer (you type in romaji and the computer changes this to kana/kanji). But mostly, it's used for the benefit of those who don't speak Japanese - you'll see it on signs in train stations and on streets, and in Japanese-English dictionaries and Japanese textbooks. Most Japanese people don't really use it except for stylistic reasons.
If you're wanting to learn Japanese, it would thus benefit you to learn the kana and kanji instead, unless you're planning to only speak Japanese and never read or write it. But really, it's worth it. Most decent Japanese text books will stop providing romaji after the first chapter or two so you don't grow dependent on it.
In my own Japanese course, I notised when trying to learn hiragana that my eyes were drawn to the romaji, because they were more familiar to me, until the textbook stopped providing them and I was forced to learn the kana or fail my class. If the romaji had continued to be provided, most likely it would have actually hindered my learning of Japanese. As it is now, I can read Japanese faster and more fluently in kana and kanji than I can in romaji.

Learning Japanese writing can look intimidating. To start, you've got the kana (hiragana and katakana) - two syllabaries (one character per syllable, rather than one per sound like in an alphabet), which means that not only have you got more characters, but also you have to figure out which to use when. The hiragana are used for grammatical functions in a sentence and for any native Japanese words that haven't got kanji, while the katakana are used for loan words and for emphasis. They're actually rather easy to learn - there are loads of apps and YouTube videos out there that will teach you both of those and they should only take a week or so of studying before you're reasonably comfortable with them.
The kanji are where Japanese gets difficult. These are the Chinese logographic characters and there are thousands of them. As of 2010, there are 2,136 regular usage kanji - these are the ones that students are expected to know before leaving school and that are allowed to appear in publications like books and newspapers without furigana (the hiragana reading) printed next to (or above) it. There are many more than that, but you won't see them quite as often and you'll have the reading provided to help you out. But still, 2,136 is a lot of characters to learn just to read a newspaper.
I'm not trying to be discouraging - honestly, I've found learning kanji to be rather fun, even while it's been challenging. There even more videos and websites and apps for learning kanji than there are for kana, as well as many suggested learning methods. I'll get into those later on - I'm still figuring out which method works best for me as well.