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OpenJDK should be fine, as long as it's 7 or later and meets the requirements of your Solr version. The latest release is recommended. In general, sticking with major versions that have long term support is the best option. OpenJDK 6 is known to have bugs. If you can get an Oracle JVM, you should.
Solr 7 is tested with Java 9 and should , so Java 9 should work well, and later Java versions will probably work. Earlier versions may encounter problemsof Solr are likely to have problems with newer Java versions.
Java 11, like Java 8, has long term support and will have many new releases. In most cases, it is just as recommended as 8. When Solr 9 is finally released, it will require Java 11.
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