I didn't learn with either Genki or Minna. They both have good reputations, but I have no reason to recommend one over the other. However, if English is not your first language and there is a Translation and Grammatical notes of Minna in your first language, that is a good reason to use Minna. Some people prefer the minimal English of Minna, and some prefer the extensive English of Genki.
Honsatsu (Kanji-Kana version) 1, 2. : the basic book.
Hyojun Mondaishu 1, 2 : the basic questions.
Kanji 1 2, : kanji lessons.
Bunkei Renshucho 1 2, : sentence pattern practice.
Kanji Renshucho 1 2, : kanji practice.
Translation and Grammatical Notes 1 2, : translations and notes in your language.
25 Topics to read as a beginner : reading practice.
1 2, Listening Tasks 1 2 : Probably questions to go with the DVDs for listening practice?
You would need "Translation and Grammatical Notes" in order to understand the first book. You'll have to learn some Japanese before you can read instructions and explanations in Japanese. There are other kanji learning systems out there, but if you learn kanji from Minna, you'll need that too.
Everything else is for practice. I would recommend going through it all, honestly. You can make your own practice by working with a dictionary and any native material, but exercises like these are designed to match your level and accompany the lessons which will be a lot more effective at the early to intermediate stages.
Also, what do you think of and compare the
New Kanzen Master Series and the
Nihongo So Matome Series?
These are both well-regarded test prep courses; Kanzen Master is recommended more often. I did not use any specific test prep materials for the JLPT, but those who do use them pass the test in much less time than I did.
If the certificate is important to you, I would study one (probably Kanzen Master) alongside your textbook course. If you don't care about certificates but just want to develop Japanese ability, I would not use either.
As for the other books you ask about, I'm not familiar with them. If I get a chance to look them over I'll let you know. I can say that in all my time studying Japanese I have never felt the need for a book specifically on "particles" or "verbs". Particles are at the heart of Japanese grammar and covered heavily in textbooks, likewise with verb conjugations, while verb meanings are in the dictionary.