So, the question is "how do I write a good first page and what are some examples?" I am not sure how helpful this will be, but here is what I got on how to write a good first page...
Start your story where they action starts. I see a lot of people make the mistake of starting with their main character eating breakfast or something stupid. Unless your story is about cooking, starting with breakfast probably isn't a good idea. If the story is about aliens invading, start the story when the aliens show up or immediately before they do. This will allow you do get to action or the meat of the story quickly. You can always add a flash back to what life was like before the aliens invaded later, but no one wants to read 1,000 words about how boring the main character's life is before the aliens arrive. They want to read about people getting the anal probes or whatever is happening. So many stories or shows start with the ending and flash back because they can create an exciting cliff hanger and start with action.
If I read your first page and there isn't a question that I want answered, you are risking me not moving on to the second page. Ask your self, "Why would someone even click this first link to the second page or make this first choice?" There should be an answer. Something like, "They want to know if the main characters girl friend survived the explosion when the aliens spaceship crashed into her car." Ending your first page with some sort of question, intrigue, mystery, or other incentive to move forward is critical. Cliff hangars are a really good strategy for this.
Mizal said this, but world building and exposition can come later. Save them for after your hook. I would rather see magic in action than have it explained. How magic works can come after I see some lighting magic kill a horde of goblins or something sweet. It's okay if things happen that are not totally explained on the first page as long as your story has internal logic and isn't impossible to follow without a ton of background info (like if you were to use made up words without explaining what they are with real words). Of course, your story might not have combat action, but you need to get into the interesting content quickly. This means introducing the romance element or a love interest on the first page or whatever it takes to have the story unfolding before the reader quickly.
Some sort of prologue is a good way to do this and introduce things that won't happen until much later in the main storyline as well. For example, a story about a school of mages might not have the students doing anything cool; however, their teacher might be a famous mage that battles a dragon in your prologue. Flash backs have already been mentioned, but they are a good way to add that information dump you are dying to put in your story after reader are hooked or to start in the middle of some "action" and still go back to the "beginning" later.
This is more general advice, but I think it is most important here in the beginning of your story: if you are being too wordy, make sure your focus of dedicating the most words to the most important elements of your story. Count the words you spend on the main character eating breakfast and compare it to the number of words used to describe the alien invasion (back to the first example). Make sure the word count favors the aliens that are literally what readers came to see and not the toast with jam.
Sorry if this is a bit disjointed or clumsy. I made it on my phone quickly, but I hope it helps!