Apache Solr runs on Java 8 or greater.
It is also recommended to always use the latest update version of your Java VM, because bugs may affect Solr. An overview of known JVM bugs can be found on http://wiki.apache.org/lucene-java/JavaBugs
With all Java versions it is strongly recommended to not use experimental -XX JVM options.
CPU, disk and memory requirements are based on the many choices made in implementing Solr (document size, number of documents, and number of hits retrieved to name a few). The benchmarks page has some information related to performance on particular platforms.