…could I get away with just adopting Hibernate for the simple things I need to do?
Yes
Hibernate is for ORM ( object relational mapping ) that is, make your objects persistent to a RDBMS.
Spring goes further. It may be used also as a AOP, Dependency Injector, a Web Application and ORM among other things.
So if you only need ORM, just use Hibernate. Time will come when you need Spring, and you will learn it then.
Here’s an architectural view of Spring:

And this is Hibernate:
