Hm. I believe there is Quicken, and then, a separate and different program, QuickBooks. You are, from your post, referring to QuickBooks.
QuickBooks is an excellent program, tho as all programs do it has its drawbacks, and it's fairly easy to use. It is, however, a bookkeeping program (though not one that all accountants like), so one has to take some care in using it in order to not misuse it
It would be a good idea, if you are going to use QuickBooks, to have your accountant give you some guidelines as you set it up. Some things I run into when people are first setting it up:
1) Your local music store, where you buy books, isn't an Expense Account. The expense account is called "teaching materials" or something similar. The music store is a vendor, and you write checks to the vendor, from the teaching materials account. Similarly for recital hall rental, etc.
2) Set your customers up as customers, not Other Names. This way you can invoice them, and know how much they owe you. Your customers aren't Income Accounts. Your income account is Teaching Revenue or similar, and your customers' money is deposited to that account.
3) If you do invoice customers, use the Receive Payments button for their payments, and deposit the payments. That way the invoices will show the correct amount due.
4) Keep your personal and business "companies" separate in QB. You can write checks to yourself from the business accountant to deposit in your personal account. Check with your accountant about what account to use to do this in the business company.
I believe that Quicken uses the word "category" for that which QuickBooks/accountants call "accounts."
And yes, QuickBooks Pro will do anything you need, and $70 is an excellent price for it.