A few thousand dollars a month is a modest budget if you want to outsource this. Try negotiating price if there's a vendor that does everything you need.

If you only need to analyze <1B events at a time, then an old-fashioned relational database is fine. Beyond that, CitusDB, Redshift, and Vertica are analytics databases that might be in your price range.

Bigger mobile publishers will usually consider analytics a core competency and handle it in-house; if you continue to grow you'll quickly reach a point where it's no longer possible to outsource this.