You might find this comparison of textbooks useful:
http://rtkwiki.koohii.com/wiki/Comparison_of_Japanese_Textbooks_Table
I've personally used Genki 1 and 2, and learned a lot from them. I'm currently working through "An Integrated Approach to Intermediate Japanese" (commonly referred to as "Genki 3" by other learners as its from the same publisher) an am enjoying it as well.
As for kanji, there are a lot of ways to learn it. The more controversial--but one that worked for me--method would be Heisig's method. I did a short write-up about it in another thread on this site if you're interested:
http://japaneseclass.jp/bulletin/thread/504
If you find that doesn't suit you, however, there are other ways to tackle the kanji. Most will recommend finding a list of radicals (the individual parts that make up kanji), getting to know them, then learning kanji along with vocabulary. Textbooks like Genki offer writing sections to help pick up kanji relevant to the current chapter.