I want to use Apache Solr for faceted navigation of my D6 site(s), but I'm unsure of the resource requirements for it. How do I check if my VPS can cope with implementing it?
This is not the most complete answer but no one else has stepped up so hopefully this can be somewhat helpful.
I would say that the biggest potential issues on a box that size would be running out of memory and disk space. You can allocate memory to your java vm to mitigate potential memory issues. Solr is under load when indexing and retrieving search results (obviously). You can mitigate the indexing load by indexing in small batches. Though in terms of memory footprint if you are substituting solr with normal Drupal search your load on apache/mysql will be greatly reduced.
I would say that I've run multiple solr instances with a higher load than you are describing on a 1GB VPS.
You may get a more detailed answer if you go to ServerFault or the Solr mailing list and share the solrconfig.xml and schema.xml files from the ApacheSolr module.