OK, I have decided to give them a try for a few websites. I have signed for a Lite Plan for two years, price just below £ 100. Here is a summary of my first experiences:
1) Subscribing to the plan was easy and fast. No problem.
2) The control panel is detailed and can be navigated fast, but very different from cPanel or other control panels I am familiar with. It is not difficult, but there are things that are different, and it just takes a little time to understand where everything is and how it works. Probably people who want to configure everything by themselves will prefer cPanel - but for most users it is fine. (When I contacted support - see below - they told me they feel their control panel is dated and a new one will be implemented this year.) In the panel, there is also a window with the status of all services.
3) Adding a domain name to the hosting plan is very different from what I have experienced with other hosting services. You need not to add the domain, but to "import" it ("import" does not mean "transfer", but just adding a domain registered with another registrar). This "import" is not instant: I have now added two domain names, and it took between one and three hours for each of them. Apparently, they check each domain name manually before adding it. Once the "import" is done, user is invited to switch the nameservers to FastVision if not already done, but it is posssible to tick a box in order to proceed first with FTP transfer - and it is easy to check how an "imported" domain looks before switching the DNS. Everything worked very well, one should just be aware that adding a domain name takes a few hours and is not instant.
4) Due to a misunderstanding regarding that aspect of the panel, I contacted support. It was Saturday evening, European time (FastVision is UK-based). I was fearing the worst... but I had a very good surprise. Within 30 minutes, I had a reply from support - and it was not a reply by somebody who did not understand: but it was a clear, personalized, helpful reply, nothing automated. I contacted them again 30 minutes later for another problem (a folder I had accidentally deleted and I did not manage to recreate); within a few minutes, I got a reply telling me they had checked, at which time the folder had been deleted, and offering me to recreate it for me. I agreed, and ten minutes later I had a message telling me the folder had been recreated. Each time, polite, helpful, caring. Wow: that impressed me! I had contacted the same day a well-reputed hosting support in the US, where I have been a customer for years, and they were by far not as helpful. So I can praise FastVision support (and I didn't tell them I intended to write a report about my experiences on NamePros!).
5) Moreover, I have checked: they have a street address, they have a telephone number, they have a fax number. This is not someting I find with every hosting service.
So I can say my first experiences have been very good. I thought it was worth sharing. Of course, in case I have other (good or bad) experiences in the future, I will share them too.
I hope it can be helpful.
