To put it in a simple way I listed some options from best to less attractive:

1. Best: self publish with your own budget.
2. Partner with another self publishing developer
3. Self publish using mostly PR and Word of Mouth tactics
4. Use a tier 1 Publisher (DeNA, Gree etc)

Why I listed it in this order:

Self publishing with your own budget allows you to control all the ARM model elements (Acquisition, Retention, Monetization) and optimize the game metrics to the exact target audience. It will give you the expertise in house to publish games which is critical to success int he long run and with other games. It does come with a cost of money and a learning fee unless you bring in someone already experienced. But long term it's the right way to go.

Your second best option is to partner with a good developer who already knows to self-publish games, run campaigns and optimize them. They could also partner with you on the marketing costs in exchange of some revenue (after they cover the marketing expense). This means they'll do a good job and will give you the opportunity to learn how to self publish. Of course, who you do the deal with is critical.

If you don't have a big enough marketing budget and no one experienced to hire, you can try to run a word of mouth campaign. This means means you'll need to find a unique feature in your game to make a big story out it and then push it to the media. This can be unique game story, unique visuals, unique gameplay - anything people could relate to and talk/write about. Monument Valley is but one example. It's still a lot of work, though, don't make a mistake.

Last option is going to a publisher. Only do it if you have absolutely no marketing budget, no marketing expertise and if the game fails it won't kill the studio. Because chances are, it won't score big. And I'm talking about the big, serious, tier 1 publishers.

The good publishers will be able to guide you a bit on improving your game and will give you the right KPI goals to aspire to. Most publishers still don't have a clue about how to do it right and will just confuse you, the good ones at least *knows* what they're talking about.

And still, publishers will only care about your game if it'll be an instant hit. It if will, they'll put the budget, the right account manager and push the game seriously. That's the optimal scenario.

In most cases, your game will achieve moderate to good KPIs but not one of an instant hit and this will happen: they won't spend money on publishing it, and will drive traffic to it from their other games. They won't be able to tell you who these players are, so you won't even be able to optimize to the target audience. They will provide you access to their stats system that will give you a lot of vanity metrics but won't allow you to control the A part of the ARM model, rendering the whole funnel useless.

Bottom line: Do your best to self publish, or partner with a good self publishing developer and learn. And good luck! :)