I'm in the US, but meet a group of people in Kitz once a year. There are several Brits in the group. They usually fly to Munich, take the local train (S-Bahn) to the Munich Hbf (main train station) where we meet up and take a 2.5 hour train to Kitz. If you chose the right train (there are usually one or two per day), you can avoid having to change in Worgl. Usually, these direct trains run only the Kitzbuhel Hahnenkahm station (not the main station). From there you can walk to anywhere within Kitz or easily find a taxi. If you chose to arrive on a weekend, the trains can be very crowded during ski season - book a 1st class ticket with seat reservations.
We usually stay at Hotel Pension Heiki in Aurach - a bit outside of town, but a nice little place with a friendly staff. There is a ski rental shop with excellent instructors, a bar and a couple of restaurants (at the Wiesenegg and Heckenmoos) close by, but not much else. While there is no direct lift access from Aurach, the SkiBus runs frequently and stops right outside and provides <5 minute access to the nearest lifts. Once on the mountain, you can reach any other part (except the KitzbuhlerHorn) via pistes and lifts. Getting to the Horn requires another short bus ride. When the snow is good, you can ski right down to Aurach on piste 33 (Giggling)