Would elasticsearch or RavenDB be better for fueling a statistics engine/random forest?
Ravendb embedds quite nicely into a .net application and also allows you to create full text (embedded) lucene.net indexes. Given your constraints on the hosting elasticsearch won't be a viable option since you'll need it to run as a service alongside of your MVC application. 

Lucene.net does not support facets out of the box but ravendb comes to the rescue here too:
http://ravendb.net/documentation/faceted-search

Ravendb also allows you to control your lucene.net analyzers quite nicely:
http://ravendb.net/documentation/how-indexes-work

Disclosure: I'm the author of the elasticsearch .net client NEST so if anyone would try to sell you Elasticsearch it be me :)