If you start early you have one thing in your favour: time. Choose the right vehicle and you can watch your investment grow through the years alongside your child. If a child is young you should look for aggressive growth from your investment.
"Much will depend on how much you have to invest," says Nigel Barlow, head of research at Countrywide, a financial advice network. "If you have pounds 10 or pounds 20 a month spare you may be better off taking out a friendly society baby bond. If you have much more, then you should be looking at a more varied portfolio."
There are more than 300 friendly societies nationally and baby bonds are one of their most popular products. These allow you to save up to pounds 25 a month and pay no tax on the proceeds. The disadvantages are high charges, and you will need to hold the bond for at least 10 years to see a decent return. Cash it in early and you will be hit by penalties and may get back less than you put in.
Nevertheless, baby bonds remain popular and are a good way of setting up a regular savings account. The larger friendly societies include Tunbridge Wells Equitable, Family Assurance and Liverpool Victoria.
Mr Barlow says that although a number of investments are cleverly aimed at people investing for children, they may not be the most appropriate.
"You are looking for good long-term growth. It can be easy to get lulled into a false sense of security by children's products when the investment performance may actually be mediocre," he says.
Donna Bradshaw, of financial advisers Fiona Price, agrees. She says using your PEP allowance or, after 6 April, a new individual savings account (ISA), is the best and most tax-efficient way of investing for a child.
You cannot take out these investments for somebody under 18 so the investment must be part of your or your partner's allowance. For PEPs this is pounds 6,000 each and pounds 7,000 for ISAs in the financial year starting 6 April (falling to pounds 5,000 thereafter).
"Most people aren't so wealthy that they use all their PEP entitlement, which is pounds 12,000 for a husband and wife, so this should leave scope for the children," says Ms Bradshaw. "If you have used your limit up you can still take out a unit trust on behalf of your child."
Ms Bradshaw acknowledges that many parents prefer to set up a regular savings account with a building society. "There are some tax advantages but a savings account is not going to give a startling performance."
The figures bear this out. If you had invested pounds 1,000 in a building society deposit account in January 1989 your money would have grown to pounds 1,622 after 10 years, while that same investment would now be worth pounds 3,368 in a typical PEP.
Children can have a savings account in their own name (unlike unit trusts) and a balance of pounds 9,000 before they start paying tax on the interest earned. You will need to fill in form R85 to claim this.
Savings accounts aimed at children include Birmingham Midshires Smart Start, which pays 6.20 per cent on a minimum investment of pounds 25.
Unusually, this account can be held until age 22, while most children's accounts must be closed at 18 or earlier. The Britannia FirstSaver pays 6.75 per cent on a minimum balance of pounds 1 for children under 17.
Another option for children under 16 is a National Savings Children's Bonus Bond. The current bond (M issue) pays 4.25 per cent interest after tax, fixed for five years, with the minimum investment pounds 25 and the maximum pounds 1,000. Rates have been cut and Ms Bradshaw is sceptical. "National Savings are not worthwhile at the moment," she says.
Some stock market investments are aimed at children. The Invesco GT Rupert Children's Fund has a low minimum annual investment of pounds 50 a year or pounds 20 a month. The initial fee is 5.25 per cent with an annual 1.5 per cent management charge.
Edinburgh Fund Managers has a trust called the Saving for Children Plan with a minimum investment of pounds 20 a month. You can also designate a stock market investment through the Flemings Share Plan.
Brian Dennehy, an independent financial adviser, says most of his clients investing for children are grandparents. "The parents are usually skint as they have spent most of their money feeding and clothing their offspring."
People putting in lump sums often invest in protected stock market funds, he says, which put a limit on any potential losses over 12 months.
Mr Dennehy says the stock market is the ideal place when investing for children because this is where the longer-term growth opportunities lie. He is less convinced by the alternatives, such as with-profits bonds or endowment policies.
With-profits savings plans, available from life assurance companies, are relatively low risk and accept small amounts, as low as pounds 20 a month. Endowment policies combine life assurance with investment and charge a regular premium for a fixed term - which could commit you to a plan you may not be able to afford at a later date.
"I cannot see any point in either of these for most people. You can replicate the returns in protected stock market funds, which give you much more flexibility and visibility," Mr Dennehy says.
Contacts: Birmingham Midshires, 0645 720721; Britannia: 0800 132304; Edinburgh Fund Managers, 0800 838 93; Family Assurance, 01273 725272; Flemings, 0500 500161; Invesco, 0800 010310; Liverpool Victoria, 0171- 405 4377; Tunbridge Wells Equitable, 01892 515353.