Houston we have a problem

There are a large number w/o digital optical, analog or headphone jacks, especially on some smaller, bargain models. RCA audio output is mostly going the way of the do-do bird on newer HDTVs. that's for certain. You definitely missed the memo(!) wink

The OP's first sentence is 'we are searching for a TV'. While I'm with you, TV before converter is usually how it progresses 8-).