Be aware up front that most small businesses fail. In games that number is much higher than in other fields. Business is tough, the games business is double-tough.
For brick and mortar businesses, let's take a restaurant for an example, you can build the place, have an awesome menu and staff, get some regular customers, advertise to all the necessary places, and do everything you are supposed to do... and then fail. The same is true in games; you can build a portfolio of quality games, have all the business requirements met, market to everybody, and do everything RIGHT, and still fail as a business.
With that in mind...
Basically, what will I need to do to start a game business (no clients comming in to house ect), copyright/trademark our name.
There are two parts.
There is the general business stuff that everyone must do. You need to register with various government agencies, pay taxes, and operate as a business. You can visit SBA.gov and your local SBA office for tips on going through that red tape.
Then there is the game industry stuff you must do. Part of that includes making great games. In my experience making the game is the easy part. Developing and testing a game is about 1/3 of the effort and cost. Game businesses do not survive on a single game, you need to develop a portfolio. Advertising and marketing and promoting your games, actually getting customers to buy the things, generally requires more effort and more cost than development. If you think making a game is hard, enticing people to buy it is that much harder. It is often 1/2 of the cost, sometimes more. The remaining 1/6 goes to supporting your customers the various other costs of doing business.
Most game startups fail. If you don't want to fail you need to study the industry and learn how business works. Making games is fairly easy. Running a game business is hard.
There are also many thousands of books on the subject of starting your own business. I strongly suggest you read as many as you are reasonably able.