We're looking at flying SQ into DME and then leaving the next morning on LH to FRA. Not sure if they would be split tickets. Either way, we'd like to visit Moscow in the afternoon on the arrival day.

It's unclear to me whether we need tourist visas or transit visas. If the former, what do we do for an invitation -- I assume we'll stay at an airport hotel. Do we just get our invitation letter from that hotel? What else should I be thinking about? Since the cost is the same between a transit and tourist visa, it seems like we might as well go for the tourist visa and maybe even a three year visa in case we return.