I prefer to fly BA (a three class 767) to Almaty and then Air Astana up to Astana. Business class on Air Astana is good and economy is fine for the short connection ALA-TSE. Connections times are not bad, although the lounge in Almaty is dire. When I looked last LH and Austrian (no flat beds) had awful arrival and departure times and you still have change in FRA or VIE. The BA flights not only provide civilised timings, you get Avios, generous tier points and a flat bed in J.

Your choice of hotel will depend on where you need to be in the city. I suggest you check Trip Advisor for the latest reviews