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Oracle provides this comparison page: Oracle Database - Comparisons | Oracle Database | Oracle
If Oracle is supporting only TM ART, then there is no need for Enterprise Edition. However if the same RDBMS is being used for other applications you will need to ensure that it can scale to fit your needs. You'll see from the comparison page that Standard Edition has some limitations not present in Enterprise Edition.
You are correct about Express Edition being unsuitable. The 4GB database size limit is too small for anything but the smallest trial configuration of TM ART.
From looking at the list, the only thing I see in Standard Edition One which would affect TM ART (other than scalability) is the absence of Oracle Real Application Clusters (RAC). TM ART supports RAC but does not require it. If you want that as an availability feature then you should avoid Standard Edition One.