Great questions! Here's my two cents.
Starting the Company
Seeing that you've already secured a domain name and necessary assets, I would suggest starting the process of creating your company. Depending on your state, it could take a few months for the paper work to finalize. Different states have different forms, regulations, fees etc. I find the easiest process is to hire a legal service to handle everything for you. It ups the costs a little but avoids all the hassle. For instance, many states require an official Operating Agreement form. Also, the legal service can act as your Registered Agent then. I believe that's a must for most states.
There are many online legal services to pick from. I suggest one of following:
What Kind of Company
There are certainly a lot of choices here but for sure you want to start an LLC. It's great for tiny start ups and handling taxes is a breeze...relatively speaking. As an LLC your team can all be considered "members" of the company. You can think of members as part owners. If you want to be the sole owner/member, that's fine but then you'll need to start worrying about paying employee wages which adds further complexity.
Company Type Differences
The big benefit of an LLC comes with taxes. All company profits are distributed directly to it's members. This is called pass thru taxation. That means the company itself doesn't pay any taxes, only it's members. Members still file a standard 1040 tax form but ensure to claim the income received from the LLC.
The only difference then comes with paying quarterly estimated taxes. This is standard for any company, sole proprietary, or even for independent contractors. Basically, 4 times a year you must pay taxes on your estimated profits for that year. Then when you do your final "normal" taxes you determine if you over/under payed. Trust me, you want to over pay. Here's a great link that talks you through estimated payments: Estimated Taxes. Remember, that's only for the feds. You have to do this also for state and local.
Estimated taxes brings one important lesson to the table. Setting aside a chunk of your revenue for taxes. If your game pulls in $1000 dollars in one month, you NEED to set aside a percentage of that to give to the government. Personally, I have to set aside 40%! And no I'm not even making close to 6 figures.
I'm sure there are great resources for doing this, however I do all my estimated payments by hand. Trust me, it's far easier then doing normal income taxes. When you are tiny, this is trivial. Larger companies will be different. Hiring a tax service is a viable option but (in this case) the hassle is not worth the cost.
Since I'm only one person, there isn't much to track. I'd imagine the same would be for you and your team so I would just use a simple spreadsheet. Any purchase or expense for the LLC is recorded there and later used to determine your actual profits. Of course, you can just get a company credit card and always use that to track expenses instead. Just make sure the CC company maintains a billing history for over a year.
Otherwise you can use whatever tax service for handling the end of the year taxes. Such as H&R Block or TurboTax.
This probably sounds very overwhelming. Especially when it comes to taxes. It'll probably be rough in the beginning. The initial learning curve is somewhat high but once you get a handle on things, it's not too bad and becomes second nature eventually. When I went through all this, the most significant thing I learned was just how much the government taxes add up. As an employee, you don't see all the additional taxes a business must pay on your behalf.