The very first thing you need is a design doc. You need to write the entire game design concept down, from start to finish, in great detail, as if explaining it to someone who has never played a game in this genre before. Ideas are a dime a dozen, but coherent game design docs are not.

If you can't describe your game via a design doc, you haven't thought the design through enough, and no experienced game dev would even touch your pitch with a 10 foot pole. You're talking about using someone's time to make something for you. If you're looking at hiring someone for pennies, which it sounds like, you'll need to really sell them on the game design concept. If you're not paying them upfront, then you better be revenue sharing, offering options in your corp, on top of whatever minimal wages you're going to pay.

Further on this vein, how are you going to recoup your expenses that you pour into this game? A neat idea you like isn't necessarily just going to sell. Will you sell the game, or is it free to play? How will you monotize the game. Will you use in app purchases? Ads? What incentives are you going to give to players to purchase items or view ads? How are you going to charge players and collect the revenue? Do you have a corporation that is set up to receive this money, with a tax ID and everything else you need? Do you need online authentication mechanisms? Is it a mobile game, or web based? Both? What kind of user authentication will you use? Is that authentication platform agnostic?

Have you ever worked on a game before? Have you never seen an artist and engineer interacting, to polish animation and choreography, tweak character models and animations in order to get something to look just right, or correct a buggy or hitching animation?

Game development is a big huge rabbit hole that you can fall into. It sounds like you don't quite know what you're getting into, which is ok, nobody ever really does at first either. But you're looking to hire engineers, people who went to school for this discipline for years to gain the knowledge they have.

It will take longer than you think, and will be much more expensive than you anticipate. Be prepared for this, or you will fail.

I wouldn't think of working on something like this with anything less than a full time developer, a part time artist, a part time PM, and a part time game designer. A lot of times a dedicated artist or programmer will also split the game design duties, or one will assume the role. But they'll not be as good as a dedicated and seasoned game designer, and so your project scope will blow out after every major milestone. Scope creep is real, and kills projects.

I don't mean to sound like a jerk about all of this. But everybody in game dev comes across pitches like these at least once a year. Nobody takes them seriously, because they're rarely well thought out and are riddled with red flags.

Anyway, without a design doc and the above questions answered, I wouldn't even know where to begin to start with putting a quote together. Someone above mentioned 10k/month per staff member, which is roughly in the right ball park. I don't think you could get a rough first pass, feature complete mvp made for less than $200,000. But I haven't seen or heard of a single aspect of the design, other than you expect something like Clicker Heroes 1 launch level polish.