First of all, congratulations! Getting a first draft done is a major accomplishment, and you should be proud of yourself.
Now, what to do with the darn thing.
Do not....I repeat, DO NOT send it off to a publisher. That's the fastest way to rejection you can imagine.
Here's my advice.
Put it away.
For at least 6 weeks. Preferably more. And work on your next book. (Or a couple of short stories. Whatever. Just Something Else.)
Then pull the manuscript out, sit down, and read it the way you would read a published book. Don't start changing anything, except possibly typos. (Tho' it's easier just to make checkmarks in the margin on typos. That way you're not interrupting the flow of the reading much.) Make notes about important things that you think need changing in a notebook. BUT DON'T ACTUALLY START REWRITING!!!
Once you've read it through, THEN start rewriting.
Why did I say not to start rewriting until you'd been through it once? Because there will be loads of things you've forgotten about (I know this sounds nuts, but it's true!), and any rewriting you do before refamiliarising yourself with the whole manuscript could break something later in the narrative. You don't really want to waste your time by rewriting, then needing to restore the original. (Been there, done that, have the t-shirt AND the tattoo!)
If you're planning on getting your manuscript critiqued, once you've done this draft of rewriting, chances are that it'll be ready for critiquing. You don't want to have raw stuff critiqued, nor stuff that you've worked so hard on that you'll find it hard to make suggested changes, even when you know they're good suggestions. (I'll write another bit about the critiquing later.)
I don't use a checklist. (But for those who might want some tips on things to look for, I'll post something soon.) I just read, looking especially for holes that need to be filled. But then, I'm the sort of writer whose first drafts are too sparse and need to be filled in. If you're the sort of writer whose first drafts are too bulky, you'll be looking to see what can be cut....chapters, scenes, paragraphs, sentences, words that don't move the story forward in either action or characterisation.
When you start sending chapters for critique, proofread them one last time....JUST looking for typos and such, NOT rewriting....to make sure that people aren't focusing on writing boo-boos and are instead focusing on what makes the story work and what might make it work better.
Good luck! And congrats again!