What's the best way to select the minimum value from several columns?

There are likely to be many ways to accomplish this. My suggestion is to use Case/When to do it. With 3 columns, it's not too bad.

Select Id,
       Case When Col1 < Col2 And Col1 < Col3 Then Col1
            When Col2 < Col1 And Col2 < Col3 Then Col2 
            Else Col3
            End As TheMin
From   YourTableNameHere

Using CROSS APPLY:

SELECT ID, Col1, Col2, Col3, MinValue
FROM YourTable
CROSS APPLY (SELECT MIN(d) AS MinValue FROM (VALUES (Col1), (Col2), (Col3)) AS a(d)) A

SQL Fiddle

SELECT ID, Col1, Col2, Col3, 
    (SELECT MIN(Col) FROM (VALUES (Col1), (Col2), (Col3)) AS X(Col)) AS TheMin
FROM Table