I am in a conference and sight-seeing in D.C. late January, motel just south of the mall. Which of the three services is the best fit/
The second one.
I think you'll want to specify the three services you're thinking of. And seeing as you're staying so close to the Mall, the Circulator bus is a great choice for sightseeing for just $1/ride, and Metro subway would also work for most visitors.
Metro if it is one of the choices.
I cannot tell what options for are looking for or what the options are. But assuming you are looking to site see on the mall, The circulator gives more of a door to door experience between museums and monuments if you do not like longer walks.The metro stop closest to the action is Smithsonian but it’s quite a walk from there to some museums and monument ( one mile)
I doubt that it's a motel
There aren't any motels in DC just south of the Mall. There are only 4 hotels I know of in that area: The Mandarin Oriental, the Holiday Inn Capitol, Hyatt Place and Residence Inn, both closer to the freeway. If it's the Holiday Inn, that's good as it's the most convenient. If you are in a motel, you might say which it is, as you may have been misled to its location, as I think it would have to be across the river to the southeast, such as Suitland or Congress Heights?. that could affect your choices. There are some motels over there.
Or the OP is just one of those people of a certain age who refer to motels and hotels interchangeably. I know several of them.