For hosted systems, the only one I can recommend is Kayako (http://www.kayako.com/) - this is a full featured customer support system which includes ticketing system to log and monitor customer inquiries, knowledge base and live chat. We are using it for our business and have clients using it for customer support and very happy with it. There is a self-hosted version of Kaykao which can be installed on your server and a version which Kaykao will host for you (this way, you do not have to deal with extra security issues, upgrade and maintenance for that system but it gets expensive after a certain number of staff users).
For a month to month hosted version, there are some reliable services and you do not have to worry about security here because that system will not share the same server as your store. We used Liveperson (http://www.liveperson.com/) before - this is basically the standard in live chat solutions. It's a bit more expensive than the rest (but if you ask them for a discount - they can give a very nice break on the monthly cost).
I would stay away from cheap systems (they have problems in different browsers and people get disconnected all the time) and I will not suggest installing any free software on the same server as your store - just invitation to a free meal for hackers.