And here I would advise you to use 1C. I have experience with different small Internet shops, so 1C for them it was always too much and too difficult. Tech support doesn't have to involve a programmer.
If you are used to web interfaces and logic provided by modern web services with 1C you will have to work hard.
I would suggest the maximum to maintain records on the web, in 1C only taxes and accounting. The benefit of 1C convenient and intuitive for accountants.
But if you say you are already in tax accounting, it is not clear why you can't keep a record of settlement there?
Here I wrote a comparison of UNF and UT, view.
My summary to try to find a solution on the web. If nothing happens, then 1C.