The answer varies depending on the customer profiles, the product, the extent of competition and what the customers are really looking for. We can chat about this and come up with a tailored strategy.
But to answer your question in a generic way...
Your question mainly is about lowering switching costs. In short, if pricing is the barrier, giving it for free might or might not let customers try you out. And once they try you, it is really important for you to retain them with your value, or else someone else will offer the same service for free and the customers will shift.
Why would any customer want to use your services? They will, only if they know about you (see point 1), and if they see any value in your services (see point 2).
1. You need to make sure people know about you. Blogs, content, ads, be something your customers look up to. The next time someone knows who can solve the problem they have, they need to remember you.
2. Customers usually see if the product is valuable in terms of
functioning: (does it solve the problem?),
affordability: (does it solve the problem in an affordable manner?),
psychology: (does it give me a good feeling to use this? Like using dung vs mosquito repellants to get rid of mosquitoes)
Depending on the product, a few other factors come in.