First off, if you haven't watched GraphQL Query Language by Eve Procello, it's one of the best introductions to GraphQL out there. This focuses on the Query language itself so it is framework agnostic.
Apollo
The Apollo framework is a popular choice for managing async data needs in a React application. This is a complete state management library so there is some buy in to use the framework.
Urql
Another lighter weight GraphQL client that is worth looking at is Urql. Urql also exposes a few react hooks that will get you started Querying, Mutating, and Subscribing to data.