I just remembered that there is a new APA hotel directly next to Sengakuji station (exit A2).
There is a direct train service from NRT to Sengakuji and from there to HND.
The only caveat is knowing the timetable for those trains. Once you do, and if you feel they are acceptably timed, this might actually be one of the very easiest options for someone who is genuinely nervous about a first visit.
Sengakuji is on the small scale compared to other stations and is within one of Tokyo’s wealthier, historic neighbourhoods (quite close to where the current Emperor and Empress will retire to), still has a homely feel though. APAs are a Hotel chain, rooms are small but scrupulously clean and well maintained and appointed. Cost is moderate. It really depends on what you are after.
There is also a Keikyu Ex Inn at Exit A4 which would be easy to get to. Also moderately priced.
Much more is going on in the Shinagawa area, but you may want to have a walk around Sengakuji using the virtual Google Maps facility to see if this is more your pace and style.