Peachtree has been around forever, as has QuickBooks. My dad owns his own furniture repair and upholstery shop in Wisconsin, and has used QuickBooks for going on 15 years. They have their own way of doing things to a certain extent, but accountants love the capabilities it has, you can make invoices on the fly, track inventory, what have you. The only complaint I have with them is the fact that they are a little anal about servicing their product if the version you have is more than four or five years old. You can get them to do it, but you need to lay on a lot of charm and bull$hit to get through to them.
Also, in regards to doing things on computer, I know it may be a little more of an investment, but get a computer that you can use solely for the business. I've seen too many things happen to people who have run a business on the same machine they use to surf the net on recreationally. In addition, I think you've mentioned on here (I could be wrong, and if I am, I'm sorry) that you are a Mac user. I'm not bashing on Apples at all (this time), but a PC will be a better fit to use for business, mainly due to the fact that there is more software offered, and at a lower cost compared to the sometimes-hard-to-find Mac versions of programs.
Good to hear about your new business! I wish you nothing but the best!