Is tsvector the right choice for searching exact match of two words with variations like plural and singular?
Short answer; yes, a tsvector column used as an index will allow you to return matching documents with stemming and pluralization handled by the default text search configuration.

The documentation is very complete and easy to read and will give you a solid grounding in how full-text search works and a bit in managing updates to the corpus and likely issue.

There are some subtleties you need to look at, but the defaults are pretty good for most languages. Things that might give issues are mostly to do with your documents structure and quirks that might need to be addressed with tweaks to the dictionaries or stop words list ( stop words are ignored for search purposes ).