As you can see, there are virtually as many ways to do this as there are those of us who like to give advice.

It boils down to your cost-to-comfort price point. If it were me, I'd:

1) Take the Keisei Skyliner to Keisei-Ueno. There is a cheaper Keisei option but I like the speed, comfort and simplicity of the Skyliner.

2) When purchasing the Skyliner ticket at NRT, I'd buy the Skyliner + Metro combo pass, and use the Pass on the the Metro subway lines to get around Tokyo as long as the Pass lasted.

3) I'd just use a ticket machine and pay cash for the Yamanote Loop Line to get to Tokyo or Shinagawa Station for departure to Kyoto. The Yamanote is cheap and there is no reserved seating. I would probably use Tokyo Station but as noted above, Shinagawa is much easier for the uninitiated. On the other hand, Tokyo Station is almost a tourist destination in itself. With plenty of time, I think everyone should see and experience it at least once.

4) I'd pay for the Hikari shinkansen to Kyoto. Hikari has unreserved seating cars so you can walk on. The same ticket would work for Kodama but Hikari will get you there faster. It is also possible to reserve seating on Hikari or even Nozomi for a bit more security and simplicity. I would definitely reserve seats but YMMV. I would arrange the tickets as soon as possible to be sure of seats on my preferred train, probably at JR Ueno Station on my first morning there before heading out site-seeing. As a personal preference, I'd travel around mid-day so as to arrive near check-in time for my hotel in Kyoto. Since I'd be traveling around mid-day, I'd definitely buy an eki-ben lunch box at my departure station and eat lunch on the train, watching the scenery zipping by.

5) Upon arrival at Kyoto, I would buy a 2-day Kansai Area Pass for the last 2 days I'd be in Japan. I'd travel around Kyoto by bus or cab and use the JR Pass for rail travel outside the immediate Kyoto area, such as a day trip to Nara, Hikone or Osaka - and for the JR Haruka out to KIX for departure. I'd reserve the Haruka at the time I bought the Pass to be sure of a seat on the train I need. The 1-day Kansai Pass costs less than the Haruka alone so is a deal even if you don't go anywhere else. The 2-day is more but permits Pass use to Nara or elsewhere. Unlike the country-wide JR Pass, the Kansai Area Pass can be purchased in Japan.

As noted above, there are cheaper ways to do all this but they would not be as simple and secure for a first-timer. I recommend paying a bit more to get that simplicity and security. Reserved seats on the Skyliner, shinkansen and JR Haruka provide a lot of peace of mind and ease of travel.