Today, there are a large number of options to choose from. The downside to upsizing your spreadsheet to a database system is that databases require fairly in-depth knowledge, especially with regard to extracting data in queries, form construction and reporting.
You may also want to track your current spending on one sheet with columns for different categories. Some individuals will list the budgeted amount in one column and then list the actual amount spent in the column next to it.
For pure data analysis, the spreadsheet is, indeed, king. To a point...Despite all of these extremely powerful features, the spreadsheet has limitations, which tend to manifest when you least expect it. Often, Murphy's Law applies and the spreadsheet falls over when you are right in the middle of a major undertaking, like month-end or meeting a tight deadline.
You may want to create a workbook with multiple sheets for various aspects of your budget. You can have one sheet that keeps track of savings and investments and another sheet that lists your monthly bills.
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