I started with the 8th Doctor audio drama “Storm Warning.” This audio reintroduces the Eighth Doctor, as well as his new companion. It can be found on audio streaming sites such as Spotify, or possibly your local library. (I recommend checking your local library. From your profile, I see you are a fellow American. I have found the first 50 audio dramas on a library service known as hoopla (among other Doctor Who and non-Doctor Who content), so it might be worth your time to see if your library subscribes to it, as it will allow you to access the audio dramas ad free if you do not subscribe to Spotify or Apple Music. Storm Warning TARDIS Guide page
Another potential starting spot is the Lucie Miller audio adventures. These were released a few years after the Eighth Doctor Main Range Adventures, and it appears that the first few are also available on Spotify. I have not listened to them yet, but they appear to be well-regarded. TARDIS Guide entry for first EDA audio aka Lucie Miller audio The main difference between the Main Ranges and the Lucie Miller dramas are that the Main Ranges are “Classic Who” style (four ~30 minute parts) and the Lucie Miller dramas are “New Who” style (one hour, with some possibility for two parters that span two separate releases). Your preference for “Classic Who” style or “New Who” style may help you decide.
The short minisode “Night of the Doctor” is also available on Youtube, but I would personally recommend “getting to know” the Eighth Doctor in some other stories first before watching.