A limited company is a separate legal entity, distinct from its shareholders and directors. This makes it a flexible way of involving other people - for example, as investors, directors or employees. Forming a limited company is often advantageous if you plan to grow the business.
A limited company also offers you the protection of limited liability. This means that your risk of loss is normally limited to the money you invest in the business (as share capital or through a loan). To some extent, however, this benefit can prove illusory: if the business needs to raise further funds from a lender such as a bank, you are likely to be asked to provide a personal guarantee. You could also be held personally liable as a director if you allow the business to trade wrongfully - that is you carry on trading through it when you knew, or ought to have known, that there was no reasonable prospect of avoiding insolvency - or fraudulently.
On the downside, a limited company involves more administration and some costs. One option which suits some businesses is to start as a sole trader, and then form a company later on as the business grows, and transfer the business to it. In return, the company issues you with shares in itself, as 'payment' for the business.
Separately, you also need to think about the tax implications. Company profits, and any income you (or other employees) take from the company, are taxed differently from income as a self-employed sole trader (or from trading in partnership). The most tax effective business form will depend on how profitable your business is, and whether you will be reinvesting profits in the business or taking them for your personal use.