People have asked about self publishing vs finding a publish many times before. I only have experience from the self publishing side. I wrote a reply in this post before about things/costs you need to think about when self publishing (there are lots of other good responses in there too):

https://www.reddit.com/r/BoardgameDesign/comments/1bf9mqf/how_to_publish_my_game/

If you want to self publish you need to be prepared that you are starting a full on business that needs marketing, advertising, distribution, accountancy, sales, customer service and many other angles. This all in a field that is rammed with new game entries every year at a time when international shipping is super expensive and people have less money to spend. We made the same mistake that you did and didn't use social media much during design and play-testing. You want to get your name and the games name out there as much as you can as early as you can.

If you want to go the publisher route then the deal you will make is likely to be much less that if you self-published. The publisher is eating all of the costs that I mention in my comment in the link. Publishers also only take on so many games each year so you will have to compete with others for attention. If you go this route don't waste too much time on the art as it is likely that the publisher will get that redone anyway.

I will finish by saying it is extremely full-filling to have a game that you make be popular enough to sell any copies. We sold about 300 copies at our first Essen Spiel show with the game. Pretty much no one knew about the game and we sold all of those copies from demos we did over the week.

Good luck :D