Datetime column vs Date + Time columns
I would use DATETIME2 as opposed to DATETIME for any new development work at this point. If you don't need sub-second granularity, use DATETIME2(0) and you'll see some space savings as well.

From here I would start experimenting. If performance is poor just querying off the single column, I'd then try adding persisted computed columns to separate out the date and time components. This will ensure that the separated DATE and TIME columns will always be the same as the "master" DATETIME2(n) column.