What index is suitable for a table with no unique columns and no primary key

Question

alpha
beta 
gamma
col1
col2
col3
100
1
-1
a
b
c
100
1
-2
d
e
f
101
1
-2
t
t
y
102
2
1
j
k
l
Sample data above  and below is the dataype for each one of them
alpha datatype- string 
beta datatype-integer
gamma datatype-integer
col1,col2,col3 are all string datatypes. 
Note:columns are not unique and we would be using alpha,beta,gamma to uniquely identify a record .Now as you see my sample data this is in a table which doesnt have index .I would like to have a index created covering these columns (alpha,beta,gamma) .I
beleive that creating clustered index having covering columns will be better.
What would you recommend the index type should be here in this case.Say data volume is 1 milion records and we always use the alpha,beta,gamma columns when we filiter or query records 
what index is suitable for a table with no unique columns and primary key?
col1
col2
col3
Mudassar

Answer 1

Many thanks for your explanation .
When I tried querying using the below query on my heap table the sql server suggested to create NON CLUSTERED INDEX INCLUDING columns    ,[beta],[gamma] ,[col1] 
 ,[col2]     ,[col3]
SELECT [alpha]
      ,[beta]
      ,[gamma]
      ,[col1]
      ,[col2]
      ,[col3]
  FROM [TEST].[dbo].[Test]
where   [alpha]='10100'
My question is why it didn't suggest Clustered INDEX and chose NON clustered index ?
Mudassar