Grouping/sorting performance choice between bigint and nvarchar
You want to store the hash using the densest datatype possible.
A bigint is 8 bytes, or 64-bits of data.
An nvarchar storing 8 bytes of data would take 10 bytes on disk.
But how long are your hashes? SHA-1 hashes are 20 bytes long (160 bits) so won't fit in a bigint. Storing it as an nvarchar will take 42 bytes of storage if stored naively.
According to https://stackoverflow.com/a/16680423/391445 you best option is to use binary(20) so you are storing exactly 20 bytes (160 bits) of data.
Are you intending to do the hashing in the database or in client code? According to the documentation, as of SQL Server 2016 all hash algorithms other than SHA2_256 and SHA2_512 are deprecated.
But a cryptographic hash function is probably not the best choice of hash function for you if all you want is a random distribution of rows. There are many hash functions available, producing whatever length key you desire!