Murauer Märzen (Märzen=Lager), Trumer Pils, Mohrenbräu are good brands.
In Vienna there is also some Belgian style craft beer =>
https://derbelgier.at
In terms of Weissbier, Schladminger is the best somewhat big name =>
https://www.schladmingerbier.at
What's also quite popular is Zwickl, which is unpasteurized beer, many brands offer it, a surprisingly good one is Schwechater Zwickl, the other beers of this brand are nothing to write home about though.
You will sometimes also find Brewingpubs that brew their own beer, like Siebensternbräu or Salmbräu, but those don't really have the best food unfortunately.
Staro Brno, Kozel, Pilsner Urquell, Budvar are all good as well and since it is historically a shared brewing tradition they are kinda native as well.
You should definitely also try wine unless you hate wine. Austria is both a beer and wine country and has the highest joint consumption in the world btw, but the good wines imo outnumber the good beers. Typical for Vienna is Grüner Veltliner, a white wine with slight metallic aroma. With food we often have Spritzer which is a mixture of usually white wine and soda water.
In late summer and fall there is also Sturm (Federweißer, Burčak in other countries) which is young wine that's still fermenting and unfiltered. It is delicious, but some people get the shits from it.