Well, that is a rather complicated question and it depends on the size and nature of your business.
Accounting records that the IRS recommends you keep include double entry method of accounting that includes Balance Sheet and Income Statements. The main objective here is that you are able to produce a profit or loss statement that tells you how well your business has performed, that is, did you incur a profit or a sustain a loss.
The Balance sheet presents you the owner of the business with a picture of your current assets, fixed assets liabilities and owners equity.
Most new startup businesses with a minimum of complex transactions are advised to use Quickbooks or Quicken. This is a simple software program and you can easily train yourself on this program.
However, I really think that you should first consult with your CPA and get his advise as to what may be the best option for you. Also, note that certain LLC's which do not meet certain revenue tresholds are not required to produce balance sheets for tax returns, however, in case of an IRS audit they are required to produce a balance sheet.