Total billions of rows and daily millions of row insert: What database system suits best
I've worked with a 30+ billion row monthly partitioned table with page compression and 10 years of history.  The table schema was fairly simple with a datetime2(2) clustered index and 3 non-clustered indexes on varchar columns and a couple of non-indexed columns.  Storage was about 2TB and it performed reasonably well.  SqlBulkCopy was used to insert about 15M rows continuously throughout the day as data was needed in near real time.

Based on this anecdote, I'm confident SQL Server could handle your expected volume with adequately sized hardware.  That being said, I completely agree with @DamianoVerzulli that your application is an excellent candidate for a less costly NoSQL solution due to your tolerance for delay.