Pro's of a Database Only Solution:
- Less set up and maintenance (you already have a database)
- If you want to JOIN your search results with other data or otherwise manipulate them you will be able to do so natively in the database
- There will be no time lag (if you periodically sync Solr with your database) or maintenance procedure (if you opt to add/update entries in Solr in real time everywhere you insert them into the database)
Pro's of a Solr Solution:
- Performance: Solr handles caching and is fast out of the box
- Spell check - If you are planning on doing spell check type stuff Solr handles this natively
- Set up and tuning of Solr isn't very painful, although it helps if you are familiar with Java application servers
- Although you seem to have simple requirements, I think you are getting at having some kind of logic around search for words; Solr does this very well
You may also want to consider future requirements (what if your documents end up having more than just a title field and you want to assign some kind of relevancy? What if you decide to allow people to search the body text of these entities and/or you want to index other document types like MS Word? What if you want to facet search results? Solr is good at all of these).
I am not sure if you would need to create an entry for every word in your database, vs. just '%[query_word]%' search if you are going to create records with each word anyway. It may be simpler to just go with a database for starters, since the requirements seem pretty simple. It should be fairly easy to scale the database performance.
I can tell you we use Solr on site and we love the performance and we use it for even very simple lookups. However, one thing we are missing is a way to combine Solr data with database data. And there is extra maintenance. At the end of the day there is not an easy answer.