I've been using QuickBooks since 2004. I reviewed all of the alternatives, including Quicken and do-it-yourself spreadsheets, but found QuickBooks to be the easiest to use. Their technical support is very good, including when your problem is accounting rather than computer-related.
They offer several different versions, depending on your business and which of the functions you want it to handle. QuickBooks Pro is their most popular, and the one I'm currently using. It does everything I need, and lets me ignore the functions I don't need. (For some reason, the same exact product but for Mac is just called QuickBooks).
Unfortunately, they discontinued a stripped down product called "Simple Start", not to be confused with "Online Simple Start". I'm not real keen about doing my accounting connected to their website. The online products end up costing you $13/month so after 18 months you will have paid as much as if you had bought the Pro product. They may pester you to upgrade every year, but I don't see the benefit. I generally upgrade every three years ... unless I find a good upgrade promotion.
Like any accounting software package, you need to know basic money management before you start, but you don't have to really know accounting. As long as you understand how a checkbook works and at least the categories of expenses and income you'll have, you will be all set.
I really like their installation process. They ask you a few questions about your business and then set it up for the "standard" model, which should have you covered. If there is stuff installed that you don't need, you can just ignore it. For a small business, this generally amounts to bank accounts, and a list of "accounts" representing the usual expense and income categories. You can add later if you need to. I've never bothered to remove categories that don't apply. They really don't get in the way.
I just did an upgrade for my computer-phobic sister, who was going from QuickBooks Pro 2004 to 2012. After installation, it updated her current account file to the new format with no problems.
Shop around for the best price. Sometimes directly from Intuit is actually the best price. Other times, you can find better prices at Amazon or other online retailers. Also watch for sales.