Giving advice for opening pages is a lot more difficult than suggesting guidance for queries. Queries have certain rules to be met while first pages ... well first pages are more subjective. What will catch one person's attention might turn another person off. (For my query tips post go here.)
Instead of calling this ramble advice and tips, this post is more rightly titled subjective thoughts about the First 250. Ideas to consider.
Besides keeping your page clean and avoiding typos, I believe opening pages are about balance. Not too much of this and not too much of that. What does that mean?
You need a balance of exposition versus action. A balance of inner thoughts and dialogue. A balance of description against deed. And a balance of show versus tell.
In other words, you want to make sure you have action and explanation so confusion is limited. Starting out with pure action in your first pages without including some exposition will make it extremely difficult for a reader to follow what's happening. Readers will be lost and confused.
If you start in the middle of a battle and give no context of why, then why would the reader care what happens to the characters? In an opening page, having some exposition provides the reasoning and motivation. Just don't go in the other direction and have too much exposition without enough action. It has to be a mix. Things happening and short explanations where needed.
(And beware putting characters in peril before the readers can possibly have formed an attachment. It's better to form a connect with the character first and make readers care before leaping into critical danger.)
Be sure to balance description of the world around the characters and movement of the plot through action. Without description, characters seem to hang in space. Readers can't orient themselves to what is happening. Yet too much description becomes like stage directions. He stood up, and he walked across the room, and he grabbed the doorknob. Too much description usually comes at the expense of moving the plot forward.
(Don't waste a bunch of space giving a detailed description of the main character. Too much worry about the appearance of your character make them into a Mary Sue. I--and maybe others--prefer to form a picture of the main character in my head based on their personality, not their physical appearance.)
Inner thoughts help make us attach to the main character. They are a good place for voice and adding personality. It's a great showcase for things the main character can't say aloud. But you also need outward verbal expression or dialogue with other characters because nothing shows off a character like interaction. Once again balance is the key.
Oh, show versus tell, you say. You've never supposed to tell. Well, not exactly. If you don't tell at times the word count is going to be out of the ballpark. Somethings you just have to tell to shorten the story or because you'd spend the whole opening chapters in flashbacks.
Show as much of the plot and world building as possible, but these are items that must be fudged at times with exposition. But always, always show your main character's personality by their actions and words.
Don't tell us Timmy was angry. Show us by his actions. He stamps a foot. He yells. He turns red. Don't tell us Susie is a weak character and can't control her vices. Show us by having her eat two cupcakes for breakfast. Don't tell your main character has a bad coughing disease. Show by having her choke on her congestion.
Besides keeping a good balance, what else can make a first 250 words stand out?
Voice A character with attitude. A sly sarcastic wit. A heart of gold. Voice can create any of these things and more. The voice of your piece can make it stand out above hundreds of others if that voice is unique.
Unique concept If you opening page starts out in a situation like no other, you'll grab instant attention. A bank robbery. A spaceship ride. A funeral. On the other side, an ordinary opening isn't going to make readers sit up and take notice. First day of school. Waking up in the morning.
Clarity Don't overload the first pages with names and places. Like in a query, try to limit the people introduced and bring them in more gradually. Especially important if you use original names and lots of unique world building such as in fantasy.
Entice Something occurs in your first 250 to make the reader curious. A reader has to find out what happens. That can involve plot, world building, or the character's personality. Something makes a reader eager to learn more.
I hope this gives some ideas. Nothing is harder than perfecting your opening page--unless it's the opening chapter. You must entice with concept and voice and not weigh down with exposition, description and inner dialogue. Yet you must avoid confusion by having some of those things to provide context.
An opening 250 is a delicate balancing act. One in which it's impossible to please everyone. It is the ultimate show of talent and precision. Best of luck and I can't wait to see those first 250 in Sun versus Snow.