Hi Janet,
Personally, I would choose a brand name to an unknown system. Why? Well, I think that it's far more easier to learn a brand name system [i.e. they'll have online support] as well as having the option of downloading a demo or a free, simple program to get you started!

In the UK/Ireland, there are 5 main brands for accounts, they are Sage, TAS Books [you can get FREE software for both of them!], MS Office Accounts [again you can get it FREE - there's one for the US as well!], Sort My Books and The Big Red Book [both of them you get a free trial, then you pay about $300 for the software]. We also get quickbooks but not many companies use them - you can download a simple version of Quickbooks for FREE as you're in the US!
Also, find out more about the unknown system. Is it a reputable company? does it fulfill what you want it to do? all of these factors are important when finding an accounting system.
Hope I've helped!
Regards.