I just recently bought a English to Japanese and back Dictionary, but I would really like to know where to start to eventually get fluent. Should I start by learning Kanji? Or the Romanized Japanese? Any help would be greatly appreciated. Thanks.

hiragana,katakana should be learned at the same time first. They are only represent sound, and are easy to learn.
The next thing is to learn the grammar and vocabulary, during which you can learn kanji.

start with hiragana, then katakana. then the basic kanji.

after that buy a manga, or read a japanese poem or listen to a japanese song (better if you have the lyrics at hand) and pick out the kanji you don't understand and look it up in your newly bought dictionary. i find it helpful to associate this language learning with something that interests me.

by the way, i never found romanized japanese helpful. but that's just me.

First hiragana. It's important for you to know the sounds of the kanas. Every Japanese word can be written in hiragana. It's easy and what you hear is what you write. Don't get used to reading only the romaji (sound of words in roman lettering). Some books come with the hiragana reading of the kanjis. Second, katakana. It's the same as hiragana, but this symbols are used to write foreign words. They are very important since Japanese doesn't have a lot of words like spoon, hotel, card, etc. After you learn those, you can start with vocabulary and include kanjis when you can. Not every word has a kanji associated in Japanese.
You will need more than a dictionary if you want to learn Japanese. Grammar is a little hard.
Have fun.

?hiragana
?katakana
?kanji

Kyoiku Kanji
http://www.taipansoftware.com/en/japanese/dictionary/