My short opinion:
Video
h264 is the best option for compatibility. There have been free software encoders and decoders forever and IIRC all patents have expired. Basically every device you will encounter and every software system can play h264 videos and the encoders are fairly good.
AV1 is the best option for quality. It is completely free and is becoming widely supported. It will likely be supported for a long time as it is the first widely available high quality free codec. It is significantly better quality than h264 so will result in smaller files for the same quality or better quality for the same file size. Hardware decoding support has only really become common in devices that hit the market in the last few years. But most new devices will have hardware decoding.
Both of these are web-compatible as well which is nice.
Audio
Opus for lossy and FLAC for lossless are both some of the best codecs in their class, completely free and widely available. There are also both web-compatible.