We use ClientBase which is a Sabre product as our CRM. It is PCI compliant and it is where we store credit cards and other client information. There are other CRM products out there specifically for travel agencies.
I need the credit card details to make the booking. Period. Although it might be possible for the client to call it in for direct hotel bookings, I have never experienced this and wouldn't feel comfortable doing so.
I have a policy that a copy of the picture page of your passport is required for international air bookings. I would prefer if you also gave me this information for any international travel (especially nonrefundable hotels bookings and large trips) so that I can verify validity and discuss any necessary visas, etc.
Travel is personal. Everyone has unique preferences, budgets, and style - and these can shift for each individual based on the type of trip (family, business, couples, etc.). We all think we do it best, but the truth is we all do it differently. A lot of trust between advisor and client is required to make the most of the experience, and that trust works both ways.
Communication is definitely key.