Too many questions, Not enough Answers

I’ve had this idea for a children’s book percolating in my brain for a few years now.  There are so many questions about how to go about it though. 

If the average word count in a picture book is approximately 1,000 words, how do you convey what you want to convey simply enough to be impactful and engaging with so little to work with.  Then, how does one find an illustrator?  Place an ad?  Do you pay for one time illustration and then you own all the rights to the material?  Promise them a portion of any proceeds? 

How do you get the thing published?  Do you NEED a literary agent?  Or can you just publish it yourself? I suppose Google is good for some of these things.  I should probably go about figuring this all out.

*****Interlude*****
I Googled since I actually wrote this original blurb.  It was almost no help at first glance.  Websites touting cheap illustrators, websites saying don't find an illustrator--your publisher will do it for you.  Websites for self-publishing. Sometimes the internet is overwhelming with the information it provides you.
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Honestly though, I should probably write the damn thing first.  I really wish that I was artistically inclined, I’d just do it myself.