Hi meryl, Big Fish has fixed a lot of the problems that people were having including fixing the 1404 error messages that people with large Purchase Histories have been dealing with for years, which is very good news indeed. Having said that, I can understand why when something like what happened to you occurred, you would be worried that it could happen again in the future.
As far as alternative suggestions to Big Fish Games, there is Steam, which has a lot of casual games. I don't care for Steam all that much due to their refund policies being so restrictive, but obviously I am in the minority as Steam is very popular.
The other casual game website that I have some experience with is Gamehouse. I have never been a member there but have purchased some games there that at the time were exclusive to the site (specifically some time management games) but now end up being released on Big Fish as well. I have never had any issues with them, although years ago we did not recommend them due to their privacy policies which I will admit I have not looked into lately.