There are many options available for the initial NFT mint for your game — including some that have games-specific tooling.
Selling anything is both a technical challenge and one of distribution. The following sites provide this and various other services.
If you are confident in your own user acquisition funnels, you can use Metaplex’s built in NFT minting and distribution functionality called Candy Machine.
There are many possible configurations for you to use. Timing, whitelists, reveals. Customize these for your product vision
There are many ways to launch and sell NFTs. Candy Machine is an open source solution that includes a lot of configuration options. But you’re not limited by this — Metaplex NFTs can be minted programmatically or ad hoc. Feel encouraged to get creative and optimize for your product.