I have a private ssl (not shared via the hosting company) installed and things are working just fine with version 1.1.2.
If it is a real shop environment, then you definitely want a private ssl (instant ssl, comdo, etc), otherwise shoppers will get the mismatched domain name error. IE will actually suggest people not to go ahead. In real e-commerce the ssl related mismatched domain error will result in pretty much no orders coming through.
If you are not willing to pay and are just testing, I’d suggest that you get a free private ssl (from instantssl.com).
When I enabled secure url, I also enabled secure ssl for admin too. Right away, I had problems with the admin url not letting me log in. So, I had to go to the db in phhmyadmin to manually change the settings and log in.
So, I suggest that you get a free private ssl, but make sure you do not enable secure url for admin.
I hope this helps.