Starting points are usually the Eighth Doctor Adventures or the Main/Monthly Range which has several starting points of it's own.

Eighth Doctor Adventures - Similar format to New Who with series made up of 50 minute stories loosely linked to form a seasonal arc. It follows the Eighth Doctor later in his life some time after his Main Range stories but doesn't really require prior listening. This range is succeeded by Dark Eyes which is made up of stories that are very closely linked to form an arc. This series will be succeeded by Doom Coalition later this year.

Main Range - Similar format to Classic Who with 2-ish hour serials usually made up 4 episodes each which are mostly stand-alone. Further along into the range arcs start to form, particularly with new companions. The range starts by alternating Doctors and companions between stories so that you'll get something like a 5/Nyssa story, followed by a 7/Ace story, followed by a 6/Peri story, followed by a 5/Peri/Erimem story. Later on the stories start to form trilogies that have the same Doctor/Companion team. These range from being heavily linked to being completely stand-alone.

If you start with the Main Range and are unfamiliar with Classic Who then I suggest watching a serial or two from a classic Doctor to get their appearance and mannerisms down before jumping in. Easy places to jump in are with the introduction of new companions:

5/Peri/Erimem - The Eye of the Scorpion

6/Evelyn - The Marian Conspiracy

7/Ace/Hex - The Harvest

8/Charley - Storm Warning

I usually do things that require little focus while listening so that I don't get lost or have to rewind too often. Things like chores, eating, walking playing a repetitive game. I once tried listening while in bed but I ended up dozing off and having to re-listen to the story so I wouldn't recommend that.