. - There are no Payroll expenses.

Start there and get more sophisticated as your experience and knowledge grows.  

You can seriously make the same cash flow and appreciation with being a limited partnership in commercial deals (typically need 50k to invest while being sophisticated or accredited investor).

The bank account will serve as your basic book keeping until you need a more sophisticated solution like QB. 

Unless you have an attorney on the payroll I'm not going to sue.

I feel like I need to show a higher level of sophistication, and preparedness.  

Nothing sophisticated.

Need some sophisticated AI!

I'm an estimator for a large international construction company, dealing with sophisticated clients and this is the standard.

Keep in mind, other than working for the school (grad assistant type work), those on student visas can't have other sources of US income (it is pretty much forbidden on the visa - I used to do payroll software and had employers that had some want to work as temps in summer; there was practically no way to get them permits to allow non-school income).