Particles are tricky pick up one of the main textbooks and go through the drills. I think its good to get a book where you have to fill in the missing particles. I used minna no nihongo and genki and websites to learn particles.

You can learn kanji anytime I think it's good to learn a few a day.

If you don't know the particles then it is really hard to make sentence. Grammar is really important and you want to know that as best you can. it is easier to look up vocabulary/kanji then grammmar. I really think you should study the particles and really master them or it will be difficult for you in the future. As for kanji, learn that as you learn vocabulary words. 

For gramar, you should use tae Kim's guide to grammar. I think it's really useful.

I would say learn to recognize particles, but you don't necessarily need to make an effort to memorize all their meanings at the beginning. It's better to learn them through recognition so you later know what "feels" right instead of stopping to think about which particle you should use. It's probably more important to know what is a particle and what is not, so you can break up the sentence to make it easier to understand. Most of the time, when Japanese people speak, they drop particles anyway, so it would sound a bit odd if you used them all the time.

I learned ( and would recommend ) learning vocabulary before particles, and then kanji after you've gotten the hang of some of that. Its very difficult to make sentences if you have no vocabulary, and  it will be difficult to place particles without subjects and objects to organize thm around. Kanji are very necessary for reading, but knowing the meaning of the word beforehand can help you memorize them. 

well most of what I was gonna say has basically already been said but learning particles is important because it helps you to structure sentences and understand the order. Also, you may choose to learn kanji whenever you want but I reccommend you attempt to learn it once you are aware of making sentences and knowledge of different words and then when you can make sentences using particles and other things go on to learning kanji and the onyomi, kunyomi and jukugo of them.