When I set up my household budget, I started by listing categories like you have, but I also added things like insurance premiums, subscriptions, and a miscellaneous fund for unexpected expenses. For irregular costs, I created a "sinking fund," where I set aside a small amount each month specifically for things like car maintenance and medical bills. It's been really helpful to smooth out the impact when those bills come due.
For savings, I typically aim to put at least 20% of our income towards various savings goals, including an emergency fund and retirement. As for fluctuating expenses, I estimate an average amount over the year and adjust our budget during peak months.
I personally use Google Sheets because it's easy to share and update, and there are lots of free templates online to get you started.
One thing I'd recommend is revisiting and adjusting your budget regularly to ensure it fits your current lifestyle and financial goals. Have you explored any budgeting apps that could streamline the process for both of you? They might offer additional insights.