I most frequently use the following online dictionaries for translation:

1. Goo Jisho
(for new words)
http://dictionary.goo.ne.jp/

2. Eijiro Translation Dictionary
(for when I mostly understand the word, but am having trouble thinking of the “right” English word for the context)
http://www.alc.co.jp/

3. Denshi Jisho
(search by radical- for when I just don’t know how to read a kanji and can’t copy/paste it)
http://jisho.org/kanji/radicals/

4. Weblio Kobun Jiten
(for Classical Japanese)
http://kobun.weblio.jp/

I also use Google, Wikipedia, Google Image Search and the Japanese internet in general to investigate words that do not appear in the above dictionaries.

For Japanese study, I don’t believe there are any particular textbooks or methods that are clearly superior, the deciding factor is whether you put in the sizable time investment necessary to master the language. The most important thing with a method or textbook is that it doesn’t bore or frustrate you too much.