If you are off by coins, how can you be sure that you only made a typo and didn't miss a transaction? To start off, I would strongly you find a way to be precise. It doesn't matter so much in the accounting, but the habit of doing a thorough job will pay off in other dividends down the line.
- Good books mean you will understand where you money really went
- Understanding where your money went, helps you create a trustworthy budget,
- Having a trustworthy budget will tell you where you need to spend less to achieve a goal
- Having realistic goals means you can achieve them predictably
- And getting real results is a positive feedback loop that will help you continue budgeting.
Basically, do the pennies now. Tryout some free online software to save the headache of data entry.
Since my primary goal is to get you to do the budgeting, and if you really hate the coins, just be consistent in how you fudge the debits and the credits.
Always round down to the nearest whole in income, and always round up on expenses. You won't overspend this way, and your back account should have a little bit of padding because you will assume less money in and more money out.
Honestly, I do tracking in both Quicken and Mint.com, so the transaction size is no big deal to me. If I did it all in Excel, I would round to whole notes. You didn't tag your question with a country, so I don't know if or similar is available to you.