How do you keep on top of your accounts for your business?
In my consultancy business I have a spreadsheet tab for invoices and one for expenses, and try and update it every month. And then a template for calculating the p&l accounts and tax I need to submit each year. I would use an app, but never get round to sorting it out.
I really would recommend just getting an accountant and accountancy app unless your turnover is very low.
It is worth getting your ledger codes right if you get to the sort of size where you employ people (codes are how you classify your income and spending), and I would recommend the less ledger codes the better, you can always create more later.
To be honest, you should be able to find a 'dummies guide' to setting up a business in the US, I would just buy that. Read it and then come back and ask more specific starting a web app business questions. People will recommend you the right US state to incorporate in and corp structure.
I used a self-hosted instance of Odoo for my consultancy company. It worked well when I did it right. It worked really bad, and data loss when I tried to use Docker.