I completely agree with the above posts -- you could never defend a favorite of someone else. That said, I think you can be directed to some of the most widely read and studied of the sonnets and start reading for your favorite with those. My personal favorite is Sonnet 116. It is the definition of true love and every time I read it I find myself smiling at the simple truths that Shakespeare is so talented in capturing in only 14 lines.
Other favorites: 29, 30, 55,73, 129 and 144.
My favorite Shakespeare poem is Sonnet 143: “Lo, as a careful housewife runs to catch one of her feather'd creatures."
It's the stuff of cartoons: a wife chasing a chicken; a crying baby; a baby chasing its mother; the speaker chasing after the mother.
And it ends with one of the great puns in literature.
The task doesn’t seem to be asking you to explicate the poem, so your best bet would be to follow the previous advice. We could tell you ours, but you would never be able to defend your opinion convincingly based upon our answers. For the record Sonnet #18 “Shall I Compare Thee” is a beautiful poem.
In concurrence with the sound suggestions of akannan, you may be able to contrast the poems based upon poetic devices used. For instance, Shakespeare's sonnets are written in iambic pentameter (unstressed syllable followed by a stressed syllable) with a determined rhyme scheme and a couplet at the end. Perhaps, you do not care for this structure.
Other poetic devices such a metaphor, simile, imagery, personfication, alliteration, assonance, etc. may be used more in one of the poems and you may especially enjoy such figurative language. Or you may prefer the tone....There are so many things to consider that choosing the poems should not be difficult.
The nature of this task is extremely personal. Few, if any, can answer it for you because the determination of "favorite" and "less favorite" is subjective and personal. I think that you can take a couple of steps to begin this process. Initially, it will be difficult to read all of Shakespeare's poems, so I would suggest from the ones you have read, identify the one you find most appealing to you. Perhaps you understood it clearly on the first or couple of readings. Perhaps you grasped its idea or you felt that there was a clear understanding within it. Perhaps it meant something to you. Then, find another poem where this connection was not as evident. When you have found both, analyze why one worked for you and why one didn't. In this light, you might have laid the foundation for being able to identify one of your favorite and less favorite Shakespearean poem.