While I have not used Solr recently, it has evolved along with ES as a solid product with a solid community. Nothing against it; it's a solid choice and there are probably people offering to host that as well. Either way you are using Lucene. Using Lucene directly makes no sense unless you know what you are doing and have a need to do that. If you have to ask that means it's not for you.
If search is important to your use case and things like relevance, precision, and recall have real impact on your business, you should get some specialists involved and not reinvent the wheel or make all the rookie mistakes. Somebody like me basically ;-). However, that can be expensive and if search is not that critical, just sign up for one of the search as a plug in solution type products out there and don't bother running a lot of infrastructure. E.g. Elastic offers a thing called App Search and it probably covers most of the simple needs and is stupidly easy to get started with. There are several competing products probably that I can't vouch for.
You can always upgrade to something proper later. Things like mongo and postgres also have some limited capabilities here and you can get away with doing some simplistic stuff with sql even. However, there's a point where you hit a brick wall and there's something you need that is simply hard/impossible using that or where you end up reinventing a lot of stuff that things like Elasticsearch probably do better.