If it were me, I'd pay out of pocket to have someone come up with a logo and the game board or some other small piece of the puzzle as Preston said, and then you would both know if you can find one person to do the design and the illustration, and you will have something to post on kickstarter to get people excited about the project. And if it's kickstarter I would certainly go higher rather than lower. Even if you don't reach your goal at least you'll have some capital to work with.
when you create a job listing, suggested freelancers are given to you to invite during the listing creation process. Scroll through that list looking at their hourly rates and then come up with a idea of the going rate for different skill/experience levels and choose the level you want and then multiply that by the approximate hours you think it would take to do the art. Boom there's your price idea. Also, when you create the job, people will bid higher and lower than the price you list so the price you list does not matter entirely so you might not need to worry too much.
The problem is I have no idea how many hours of work this is? So I can't just multiply their hourly rate by the number of hours to come up with a number.
Here's another problem with just putting a bid out there. This has happened to me before. I estimated how much it would cost and invited a freelancer that I really, really wanted to work on my project. They declined my job becaue the bid was too low. I would be willing to pay them more but now I have no way to message them and tell them that I was just estimating how much it would cost. This system seems very flawed.
An artist charging by hour already is a bit weird to be honest.
its okay to have no idea how much something should cost or how long it takes.
i am recommending you hire an art director or senior artist to have a look at your project and give you an realistic estimate.
that will save you lots of nerves and shows you where you are standig at.
re: "An artist charging by hour already is a bit weird to be honest."
An artist charging by the hour is a person getting paid for his time, just like anything else.
Nearly all of the artwork I have commissioned on Upwork was paid for using hourly contracts. I am very pleased with the results.
I am sure you are happy by commissioning hourly.
Not going for value-based prizing is neither industry standard in the creative fields, nor is it very clever by the artist.