You may believe primary key is unnecessary, but in my experience it is critical. You may never use it.
But the database itself uses the primary key to determine PHYSICAL organization of the data. Correction: I have been corrected here - in SQL Server, the physical organization is based on the clustering index. By default a primary key IS the clustering index, so by adding a primary key, the clustered index is added and the rest of my point is still correct. But if you don't want to use an autonumber or some other primary key as the clustered index, you CAN still use some other column to cluster. You should definitely pick one, though. Check out this link: http://technet.microsoft.com/en-us/library/ms186342.aspx
primary key clustered index you risk corruption of your data. And in some cases, when it seems like totally unnecessary, adding a primary key that you don't even search on will dramatically improve query performance.
here is an excellent description of the basic indexes in SQL Server. https://www.simple-talk.com/sql/learn-sql-server/sql-server-index-basics/
Based on the basics you have given us, I would say you need something like a primary key (auto number works) that will be your clustered index, then several nonclustered indexes (on all three of your search fields), which are the typical index when you want to search on various columns that are not necessarily the primary key.
If data will be edited a lot (like when a software application is used to manage data), a lot of indexes (i.e., nonclustered indexes) will slow down insert/update/delete activity, because the indexes are updated when the table is. But if your focus is on selecting data, indexes are critical.
If this is updated in batch daily and is not part of a software system, you could have a routine which drops the indexes, does a batch insert, then recreates the indexes.
But regardless - what you want for your search fields are nonclustered indexes. Clustered indexes "cluster" an entire record around the primary key (or whatever field is chosen as the cluster basis). Nonclustered indexes are what are created when you do indexes on any other field.