Just chiming in to say there is no right way to manage a budget. The right way is whichever way works for you. Some folks here are "set it and forget it" types that let the apps like Mint, YNAB, etc. do the tracking and have everything automatically depositing into various accounts, bills paying, etc. Good for them and their well-oiled machines. That ain't me!
I am most successful when I am most actively engaged in my money management. For me that means I work out of an Excel spreadsheet where I have a chronological schedule three months in advance of each paycheck, and line items for which bills will be paid out of said paycheck. Each paycheck is sectioned out into non-negotiable savings (for you this would be non-negotiable savings AND debt repayment), bills, and variable expenses (groceries, gas, etc.) It looks something like this:
Pay Date: X
Take Home Pay: $2,000
Mortgage: $530
Car Insurance and Taxes: $70
Car Maintenance: $50
Emergency Fund: $50
House Sinking Fund/Home Maintenance: $300
Vet: $20
Power: $75
Water: $75
Cell Phone: $55
Groceries: $200
Gas: $55
Misc Spending: $200 (restaurants, clothes, fun stuff)
TOTAL: $1,680
DELTA: $320
Then once every bucket has been accounted for you can really see what is left and adjust accordingly. I have $320 left after all my responsibilities are taken care of! I can allocate that accordingly depending on my goals, needs, etc.
The main thing is that nothing is a surprise, ever. Your budget/schedule is proactive, not reactive, to the financial requirements of your life. If you pay your car insurance quarterly, you still have a line item per paycheck or per month for that, and you stash that money away in anticipation of that bill coming due. You then have a line item for that bill on the date it is due. I repeat... nothing is a surprise, ever.
Part of the way I make sure there are no surprises or that I'm running short when a bill comes due is to pay every bill on payday, whether it's due or not. If the bill is due during that pay period, it gets paid ON pay day. One other trick that I used during the debt-paydown year of my life was to partially pay certain large bills to make my pay periods consistent with each other. OR, if a partial payment isn't an option, create a separate account (I call mine "Holding") and split the bill in half yourself. I do this for my mortgage each month so that I don't have one paycheck with $1000 coming out. Think about the same concept on a smaller scale to balance your income stream.
I personally like doing it this way because I manage my income to the dollar and feel that I have a ton of control when I'm able to see everything this way and adjust buckets as needed. I have formulas that also let me see how my diligent saving will impact each bucket into the future, and back when I was in debt repayment mode, that was hugely motivating as I could see how (if I stick to the budget!) in 3 months time my debts would be smaller, or gone, etc.
Find what works for you and make it enjoyable. Best of luck!