While Romeo and Juliet is a wonderful play, whether it would be a good model for a present day relationship depends on the nature of the people involved. If the girl you wish to invite to homecoming enjoys poetry, a poetic speech or a poem written in beautiful calligraphy might be the way to her heart, but if you are not also a poetry aficionado, it could be very awkward. The main thing you should remember is that you should just be yourself.
The best way to talk to girls is actually just talking. Perhaps go for a walk around your neighborhood or to a place with nice scenery or to a nice coffee shop. If you also like horses, perhaps you could go for a ride with her. Talk to her naturally about interests the two of you have in common. Next, ask if she has plans for homecoming yet. This gives her the option of saying that she already has plans if she has a date or doesn't want to go with you, sparing you both embarrassment. If she answers that she doesn't have plans, that signals that she is interested in you, in which case you can just go ahead and ask.