The banks are always keen to attract graduates because they expect them to be good earners in the future. They will consider you for a graduate account up to three years after you have graduated.
Compare the products available in the marketplace. Ignore incentives such as discounts at shops and restaurants you'll probably never use - it's the figures that count.
Graduate accounts offer preferential interest rates on personal loans and 0% rates on overdrafts but interest rates and terms vary greatly. You need to be shrewd: Look at terms on free overdrafts; interest rates on extended overdrafts and personal loans; and fees for going over the overdraft limit.
For example, Barclays offers interest free loans up to £3,000 in year one, £2,000 in year two, £1,000 in the third year and £500 in the four year but there is a £5 a month fee. HSBC has no monthly fees but offers interest free loans of £1,500 in year one and £1,000 in year two. Check out the interest rates on extending your overdraft. For example, Abbey will charge you 9.9% and Barclays 15.6%. If you expect to need a personal loan as well, you need to compare interest rates here as well.
Beware of unauthorised overdrafts - the interest rates may be outrageous. NatWest charges 17.81%, Barclays charges 27.5% whereas Lloyds TSB will make you pay 29.8% plus a fee of £30 a day (up to £90 a month).