I just use a simple time tracking program in my menu bar to track hours against projects with short comments. Then when it's time to invoice, I go into QuickBooks and make a new invoice (you can clone an existing one for the same client). QuickBooks emails it to the client directly. QuickBooks Small Business is all web-based and pretty easy to use.
I'd recommend invoicing everyone even if you don't need to (because you said some of your clients are more informal about asking for payment). Having consistent invoices for everything in one place will make taxes a lot easier. It will also be important if you ever need to do something like get a loan or buy a house or anything where you need to show who you clients are.
If you are in the US, don't forget to pay your estimated taxes on time! If you are somewhere else, make sure you register for the appropriate local system and don't get behind on taxes.
W.r.t. estimated taxes -- I seem to remember doing the math and concluding that I'd likely come out ahead financially by keeping the money for the estimated tax payments in the market, and then paying the late fees. Does that sound incorrect to you?
I agree with invoicing everyone. Invoicing a client from your own business also helps distinguish you from being an employee, should that ever come into question.
I'd recommend invoicing everyone even if you don't need to (because you said some of your clients are more informal about asking for payment). Having consistent invoices for everything in one place will make taxes a lot easier. It will also be important if you ever need to do something like get a loan or buy a house or anything where you need to show who you clients are.
If you are in the US, don't forget to pay your estimated taxes on time! If you are somewhere else, make sure you register for the appropriate local system and don't get behind on taxes.