The first thing you should ask yourself is "what are the properties of 'Equipment'?" Can a piece of Equipment exist without EquipID, Description or Category? If not, then those columns should not be allowed to be null.
Second is "what uniquely defines a piece of 'Equipment'?" Is it the EquipID? Then that should be your Primary Key. Is it a combination of EquipID and Category? Then you have a composite Primary Key consisting of both columns. Sometimes, however, the data doesn't naturally lend itself to a primary key that can easily be joined against in a fully relational model. Therefore, you could consider the Identity ID column like you show - this is known as a surrogate key. Know that creating a primary key by default creates a clustered index on those key columns. If you go with the surrogate key approach, IMHO it is a good idea then to create another unique index on the uniqueness of your object (i.e. EquipID).
As far as other indexes go, you should further ask yourself "what columns am I going to be querying against most often?" Perhaps you will have a lot of queries like "SELECT EquipID FROM Equipment WHERE Category = 3". This would suggest that Category is a good candidate column for an index.
Finally, another good rule of thumb is to index any foreign key columns - which it appears that Category could be. This optimizes any join queries that you may perform.
A good approach to this would be something like below (quickly thrown together, not tested):
CREATE TABLE [dbo].[Equipment](
[EquipID] [nchar](20) NOT NULL
,[EquipDescription] [nchar](100) NOT NULL
,[CategoryID] [bigint] NOT NULL
,CONSTRAINT [PK_Equipment] PRIMARY KEY CLUSTERED (
[EquipID] ASC
)
) ON [PRIMARY]
GO
CREATE TABLE [dbo].[Categories](
[CategoryID] [bigint] IDENTITY(1,1) NOT NULL
,[CategoryName] [nchar](100) NOT NULL
,CONSTRAINT [PK_Categories] PRIMARY KEY CLUSTERED (
[CategoryID] ASC
)
) ON [PRIMARY]
GO
CREATE NONCLUSTERED INDEX [IDX_Equipment_Category] ON [dbo].[Equipment] (
[CategoryID] ASC
) ON [PRIMARY]
CREATE UNIQUE NONCLUSTERED INDEX [IDX_Categories_CategoryName] ON [dbo].[Categories] (
[CategoryName] ASC
) ON [PRIMARY]
ALTER TABLE [dbo].[Equipment] WITH CHECK ADD CONSTRAINT [FK_Equipment_Categories]
FOREIGN KEY([CategoryID]) REFERENCES [dbo].[Categories] ([CategoryID])
GO