Why set up a private limited company?
After all, setting up a limited company is likely to involve more administration and higher costs than if you were a humble sole trader.
Essentially, the answer as to whether you set up a private limited company concerns personal financial liability. If you're a sole trader and your business fails, you're personally liable for its debts. Potentially, you risk personal bankruptcy if the debt is considerable and you can't pay it. Setting up a limited company offers protection against this.
A limited company is a separate legal entity and as such, legally, it's responsible for its own actions. The finances of private limited companies are entirely separate from those of its owner(s). Private limited companies can have one or more shareholders, but shares cannot be sold publicly (i.e. on the stock market). Public limited companies, of course, can do this.
Providing you don't trade recklessly or fraudulently, as a director of a limited company your risk of loss is restricted to money you've invested in the company. However, you're liable for bank loans if you provide personal guarantees for that limited company.
To an extent, being a private limited company might make you more credible to potential customers, partners or investors.