For online pattern searching, I'd want Boyer-Moore with the the Galil rule for guaranteed linear search. [Due to an unfortunate accident in C++ history, Boost and C++17 skip the Galil rule, leading to O(n+m) runtime vs. O(nm).]
For offline, Burrows-Wheeler has performance linear with query string and independent of the length of the searched document.
This allows for result documents that can contain some of the terms, all of the terms, or a prefix of a term. It's also pretty fast as it doesn't need to run a linear search through the documents. I'm not sure what you mean by "classical" search algorithms, but a trie based search is a pretty standard way of doing it.
Tries led to suffix trees led to suffix arrays led to Burrows-Wheeler transform led to FM index, which is probably the best way to do an offline search.
If you haven't looked at BWT indexing, it's worth at least checking out. It preserves the advantages you speak of with linear memory cost with the search space. It's a lot more hairy to implement, unfortunately.
http://www.cs.jhu.edu/~langmea/resources/lecture_notes/bwt_a....