Selecting max record for each user

The safest way to do this is with row_number

select MemberId, ContractId, StartDate, EndDate
from (select mc.*,
             row_number() over (partition by MemberId order by contractId desc) seqnum
      from Member_Contracts mc
     ) mc
where seqnum = 1

This handles the case of multiple contracts for the same member . . . which may not really be an issue in this data.

This solution uses the uniqueness of the ContractId field:

SELECT MemberID, ContractID, StartDate, EndDate
FROM member_contracts 
WHERE ContractId IN (
    SELECT MAX(ContractId)
    FROM member_contracts 
    GROUP BY MemberId
)

See it working online: sqlfiddle