Live chat for sales is a huge yes.
For support, a hosting company would prefer tickets as it enables a tech to properly troubleshoot any issues and provide a more thorough response. However from a customer perspective, many do prefer live chat so it does make sense to have at least level 1 support available over live chat (if you have the team/resources to do so).
If you are just starting up (one-man band) I would personally recommend having live chat but hiding it when offline. Customers seeing an offline chat system is much worse than them not seeing live chat at all IMO.