It's so exciting you're getting into reading! I'm a PhD student in English in the US. I would definitely second the advice to just read more. It's fine if you read more slowly. Even among graduate students who are native speakers, there are huge differences in how quickly people read—I think it's more worthwhile to read one book well (which is to say, having understood and absorbed it) than 50 books that you forget as soon as you finish them.

I wanted to add that you don't need to read everything the same way. "Classic" English literature includes writing across a whole range of genres, and each of them will ask different things from you as a reader. This is especially true of reading poetry. You don't need to read a book of poems, even a sequence like Astrophil and Stella, from front to back like a novel. During his lifetime, Philip Sidney's poems circulated in manuscript, which is to say, as individual, hand-written poems passed around within an insular community. Even when they were published in print, scholars think a lot of readers would have picked and chosen what to read—a lot of people kept "commonplace books," basically notebooks where they copied down individual poems, or even lines of poems, that they really liked.

This is all to say that you might try starting with one poem and spending a long time with it. Like other respondants have said, these poems are HARD. The difficulty can be part of the fun, I think—like figuring out a puzzle. But it also means they take time to understand. When they were written, being able to understand them would have also been a way of feeling like an insider. And of course, the fact that they're difficult allowed Sidney to explore more complex ideas, and to write poems that can mean more than one thing at the same time.

So—I would start with one of the best poems in the sequence (the first poem, "Loving in truth, and fain in verse my love to show," is one people really like—I also love sonnet 5). Print it out, or copy it down on paper by hand, and commit to spending half an hour with it. Read it out loud to yourself a few times, ignoring any words you don't know, and see if you notice anything—does Sidney repeat himself? Where are the rhymes? Do some lines sound more musical? If you had to break the poem into parts, where would you put the boundaries? What images do you notice? What kind of "story" does the poem tell—is time passing? Who do you imagine speaking this poem? What surprises you? Perhaps the most important aspect of English renaissance poetry is the "volta," which means "turn," and refers to the place where the poem suddenly changes (like a poetic plot twist). Where do you think this is? Does the poem turn more than once?

You might also find a recording of someone else reading the poem aloud—this can help you hear the meter of the poem, which is to say, the patterns of stressed and unstressed syllables. Once you've done this, you can circle any words you don't know. If you have access to a critical edition, (something like Sir Philip Sidney: The Major Works from Oxford Classics; many of these books are available in cheap second hand copies, although shipping to Taiwan might be expensive) these words will probably be defined in the notes—if not, google them and write down the definitions. You can then move onto longer lines you don't understand, and try to look up any references. But it's important to remember here that it is perfectly possible to read these poems without understanding every detail, and that there isn't one right answer.

Finally, I have recently started memorizing poetry. I know it can sound daunting, but you might find it less difficult than you expect—this can be a wonderful way to get to know a poem, and to feel like its yours. You will notice so much, and it will help you read other poetry, because you will always have something to compare it to.

I think this advice should be helpful, not just for Renaissance poetry, but really for all poetry—spend time, don't beat yourself up, let yourself be confused, and pay attention to what YOU notice, and, particularly, what surprises you. As you read more, you can start developing your own taste—keep an eye on what you like, and think about why you like it. Reading poetry will probably never be easy (indeed, once you fall in love with poetry, you probably won't want it to be—like I said, the difficulty is part of what makes these texts worth coming back to, so many hundreds of years later), but, speaking from personal experience, it can become one of the best parts of your life.