SQL Server Partitioning - what to use for partition key?
The server spec questions should be directed to either Serverfault or DBA.SE.

For the partitioning question, I don't think you necessarily need to partition for this.

360m rows is a lot but it's not too unwieldy.  

Do NOT under any circumstances try to partition based on the last digit of a field.  I'm not sure this would even work, but it's not SARGable which wouldn't be tenable.

If you only need to do a single row seek based on a numeric key, partitioning probably will not help.

If you do decide to pursue the partition route, bear in mind to be effective all your queries need to include your partition key(s) so the engine knows which partition to check.  Otherwise it will check them all and you actually hurt performance.