You may need to understand the following things.
1. Icoca and Haruka is a package of one way ticket valid on Haruka and a IC card (Icoca). Round trip version of Icoca and Haruka includes two ticket of one way Haruka ride. This "Haruka ticket" is valid before you get out of the station gate: For example, if you use this Haruka ticket to go to Kyoto, you can't get out at Shin-Osaka station. If you go out of the station, then the Haruka ticket will be collected by the station staff.
2. After you get out of the station (Tennoji, Shin-Osaka, Kyoto etc), you can use Icoca IC card. This is a pre-paid card with 1500 yen value and 500 yen deposit. Note that there are many rail companies in Japan, and most of the rail pass are valid only for certain companies. For example JR's Kansai Area Pass
https://www.westjr.co.jp/global/en/travel-information/pass/kansai/is valid only for JR trains. You can not use Kyoto City bus with this pass, for example.
Kansai Thru Pass
http://www.surutto.com/tickets/kansai_thru_english.htmlis valid for only non-JR trains. You can use, Nankai, Osaka metro, Hankyu, Kyoto metro, Kyoto city bus, Kyoto bus etc, but it does not cover JR trains.
Icoca is issued by JR, but it is valid on both JR and non-JR trains. This is a big advantage, but please note that this is not a "pass". When you use Icoca, the amount of money it has is deducted.
3. If you stay near Kansai Airport for the first night and then proceed to Kyoto the next day, Icoca and Haruka will be nice. After using the Haruka part, you will still have Icoca card valid for 2000 yen (the 500 yen deposit will be refunded when you leave Japan from KIX). So, your Kyoto trip from KIX costs only 1000 yen. You can go with non-JR train, but it requires 2 transfers and is slower than Haruka.
4. In general, Kyoto is the "must" place for foreign travelers to Japan, but the hotel rates are in the expensive side. So you might better stay in Kyoto for sightseeing in Kyoto, but for the "base", you might better consider other places such as Osaka.
5. JR's Kansai Area pass will be cost-effective when you go to Himeji, since it is somewhat far from other cities in Kansai area, and JR train is faster than non-JR trains, especially in Kyoto-Osaka-Himeji section.
I can't say which are best combinations unless you specify the exact itineralies, but my guess at the moment is Icoca and Haruka round trip version plus Kansai Area Pass one day (for trip to Himeji). One day bus pass for Kyoto (500 yen) might be also useful.