It depends a huge amount on what your business is. I'm in the UK so the names of the company types vary but the basic structures are similar wherever you are, you have 3 main choices;
1. Sole trader/self employed
Simple and quick to set up, it means YOU are the business, it has no seperate legal identity, it requires minimal paperwork, and there are lots of tax benefits, like buying a new suit can be a business expense and tax deductible etc. Downsides if you hit any legal issues it's YOU who is in trouble, not "the company" because "the company" doesn't exist in a legal way, it is just you. Unwieldy as businesses grow and you want to employ people, well suited to small home businesses, solo people (like many freelancers), tradesmen etc.
2. Private limited company
Standard model for small to medium sized businesses. You have a small group of privately invited shareholders who all own a % of the company (like your ten family members could all give you $X in return for Y number of shares), or it can be really small, like just a couple of shareholders. The company is a legal entity in it's own right, it runs up it's own credit, debts, makes it's own purchases and you are a director of the company rather than being the company. It's fairly light on paperwork and set up if you take time and read some useful guides relevant to your country, it's a good growth model as the company can make it's own investments, take loans, contract deals etc, very flexible.
Also worth mentioning partnerships here, these are somewhere between 1 and 2 and only for businesses with 2+ partners who all have an equal share in the business, has a mixture of the above features.
3. Public company
Like a company on the stock market, really suited for big comps, you don't own your company the shareholders do, and they can be anyone in the world. Lots of paperwork and legal requirements, very complex and expensive, but it can also be very easy to raise money (just release more shares). Of course, you can also lose your company to aggressive share buyers as well.
Generally, private limited is a great model for most businesses, admin is low but it's possible to grow to any size without any changes. If it's just a small idea you want to do on your own like a freelance, go for self employed as it's so simple.
Read around online at business startup guides, and at some point you should talk to someone with specific experience in your country like a lawyer or just other business owners.
Technically freelance, but mostly at SDG Web Design