Before you make an accounting decision, talk to some bookkeepers. I recommend using QuickBooks [from Intuit]. (If you work with a bookkeeper from the outset, you may not need to buy your own software.)
Assuming everything goes well, you are going to want to be able to hand off the accounting for your business (as well as some of the accounting-related functions, e.g., generating invoices, paying bills) to a bookkeeper. And whereas every bookkeeper knows QuickBooks, their familiarity with other software packages will be hit-and-miss. I spent a couple of weeks using GnuCash, a freeware alternative to QuickBooks. It seemed fine, but I talked to a bookkeeper, and sure enough, she had never heard of it.
As the industry leader, QuickBooks also has good integrations with financial institutions for automatically retrieving your data. It’s offered as SaaS (software as a service) or as normal software. If you go the software route, don’t worry about getting the absolute latest version; last year’s will be fine, and will be cheaper.
I recommend serving as your own bookkeeper at least until you understand how your books are kept; then hand it off to a bookkeeper as soon as the economics of paying someone to do it makes sense. (Unless you love bookkeeping.)