CREATE TABLE #MinAmt
(Id int, A int, B int, C int)

INSERT INTO #MinAmt
(Id,A,B,C)
SELECT 1,1,2,3 UNION ALL
SELECT 2,4,5,6 UNION ALL
SELECT 3,0,2,3 UNION ALL
SELECT 4,1,2,0 UNION ALL
SELECT 5,-1,2,3 UNION ALL
SELECT 6,1,2,-3 

select
	ID,
	[MinVal] = (
		select
			min(x)
		from
			(
			select x=A where A > 0 union all
			select x=B where B > 0 union all
			select x=C where C > 0
			) m
		)
from
	#MinAmt
order by
	ID

ID          MinVal
----------- -----------
1           1
2           4
3           2
4           1
5           2
6           1

(6 row(s) affected)

;WITH MyValues AS (
    SELECT Id 
        ,A=CASE WHEN A > 0 THEN A ELSE 2147483647 END
        ,B=CASE WHEN B > 0 THEN B ELSE 2147483647 END
        ,C=CASE WHEN C > 0 THEN C ELSE 2147483647 END
    FROM #MinAmt)
SELECT Id
    ,MinAmt=CASE 
        WHEN A < B THEN CASE WHEN A < C THEN A ELSE C END
        WHEN B < A THEN CASE WHEN B < C THEN B ELSE C END
        ELSE CASE WHEN C < A THEN C ELSE A END  END
FROM MyValues

;WITH MyValues AS (
    SELECT Id 
        ,A=CASE WHEN A > 0 THEN A ELSE 2147483647 END
        ,B=CASE WHEN B > 0 THEN B ELSE 2147483647 END
        ,C=CASE WHEN C > 0 THEN C ELSE 2147483647 END
    FROM #MinAmt)
SELECT Id
    ,MinAmt=CASE 
        WHEN A < B THEN CASE WHEN A < C THEN A ELSE C END
        WHEN B < A THEN CASE WHEN B < C THEN B ELSE C END
        ELSE CASE WHEN C < A THEN C ELSE A END  END
FROM MyValues

CASE WHEN [longer case] IS 2147483647 THEN NULL ELSE [longer case] END

;WITH MyValues AS (
    SELECT Id 
        ,A=CASE WHEN A > 0 THEN A ELSE 2147483647 END
        ,B=CASE WHEN B > 0 THEN B ELSE 2147483647 END
        ,C=CASE WHEN C > 0 THEN C ELSE 2147483647 END
    FROM #MinAmt)
SELECT Id
    ,MinAmt=CASE 
        WHEN A < B THEN CASE WHEN A < C THEN A ELSE C END
        WHEN B < A THEN CASE WHEN B < C THEN B ELSE C END
        ELSE CASE WHEN C < A THEN C ELSE A END  END
FROM MyValues

CASE WHEN [longer case] IS 2147483647 THEN NULL ELSE [longer case] END

WITH MyValues AS (
    SELECT Id 
        ,A=CASE WHEN A > 0 THEN A ELSE 3000000000000 END
        ,B=CASE WHEN B > 0 THEN B ELSE 3000000000000 END
        ,C=CASE WHEN C > 0 THEN C ELSE 3000000000000 END
    FROM #MinAmt)
SELECT Id
    ,MinAmt=
	convert(int,nullif(
	CASE 
        WHEN A < B THEN CASE WHEN A < C THEN A ELSE C END
        WHEN B < A THEN CASE WHEN B < C THEN B ELSE C END
        ELSE CASE WHEN C < A THEN C ELSE A END  END
        ,3000000000000))
FROM MyValues