Quicken and MS Money will track most small businesses. Quickbooks is better if it is a larger one and you need invoicing and other features. I haven't stayed up-to-date, but Peachtree used to be decent and there are 2 or 3 other programs that will do the job. All are well under $200.
If you really want to learn accounting, take an accounting 101 course at your local Community College. I haven't seen a computer program yet that even taught basic bookkeeping. Accounting is more than just bookkeeping.
Michael