I learned Hiragana and Katakana within about 2 months of coming to Japan (about 4 1/2 years ago). I found some books for Japanese kids, with the stroke orders written. I memorized them one group at a time. For example, one day I memorized "a, i, u, e, o". The next day "ka, ki, ku, ke, ko" and so on. I had no job at the time so I had plenty of time. I just wrote them one by one like 50 times, while repeating the pronounciation aloud (a good point is that the pronounciation is easy for native English speakers and Fillipinos). Now, when I stepped outside, everything was in Japanese, so I could get plenty of reading practice. Since you're in the Phillipines, I recommend randomely browsing Japanese websites. It won't make any sense to you at this point, but just read the Hiragana and Katakana aloud. That way you won't forget. AIso, it really doesn't matter which you learn first, but since katakana is used to write loanwords, and many of these come from English, you'll be able to recognize the meaning of many words as soon as you learn katakana. But be careful, the meaning of loanwords are sometimes quite different from the original English meaning!

I said the pronounciation is easy for Fillipino people, if you follow the romaji next to the hiragana/katakana you can't go wrong. But actually there are a few ones that are a little hard: っ (ex:　いったーいた) えーえい おーおう あいーあえ Basically, these differences are difficult to distinguish at first for many learners.

The way I learnt them: Learn the difference between them. Then write them (stroke order, actually helps with memorisation) and use flashcards. Then write basic sentences using all of them from memory, consulting help if needed. You can learn them in a few days from scratch if done right. :) But, it depends on your style of learning entirely; try to incorporate visual, audio and kinesthetic ways to learning them. Good luck!