Most spreadsheet applications have built in formulas and functions that will do the math for you so you don't have to. You can keep a running balance of your accounts and you can have each category totaled as well. You can keep it as simple or make it as sophisticated as you please.
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.
Once you design the type of budgeting spreadsheets you want to use, it will be easy to copy it for subsequent months or years. You can also use just one sheet and create tabs for each month.
You could make money doing something you love (or like [or maybe not so much but just really good at]). It's great to see a spreadsheet come together, and usually a lot better than what you originally envisioned. Especially when the dang thing works.
blank spreadsheet templates
examples of spreadsheet packages