Yes, Vienna is the best option, as the flights to Vienna are also cheaper!
There is a direct train connection from Vienna Airport to Graz main station every hour.
3 hours train journey...
Alternatively, there is also FLIXBUS between Vienna Airport and Graz.
Train:

Bus:
Yes, @ph1102 , https://www.oebb.at/en/ https://www.flixbus.co.uk/

If you know when you are arriving in Vienna, maybe we can organise a shuttle... As some Hivians come from Vienna

cheers with a little Bit !BEER 🤠