Heading over to the Episode page the obvious place a new comer would think to start would be the pilot episode of the First Series "Moving Forward".
I would actually suggest not starting here and personally would say a far better place to start would be "Red Rising" ( Series 3 Episode One) .
The reason I say this is because within the first 8 minutes alone the basic series concept as a whole is summed up by Doctor Watson. We meet the three main hero characters Holmes,Watson and Miss Blake, the time period is explained and you will get a good feel for the series overall.
Through the course of the 50 minute episode (divided in 6 parts) some of the very key notes and arcs that have occurred within the previous two years are also raised allowing for a greater picture to be built altogether.
In addition the editing and visual appeal here is far greater than within the first series making for more enjoyable viewing.
There after finishing this episode I would say largely you could go on to continue the rest of the 3rd series or indeed then start the 1st or 2nd series and it will make you appreciate the show as a whole a great deal more and have a better understanding overall.
Alternatively one could begin with the 2010 Christmas Special Holmes In Time For Christmas which is fairly standalone as a retelling of a Great Hiatus Year tale set in 1893
OR any of the spin off "The Mary Morstan Mysteries" episodes which take place 130 years prior to NPLH. Though there is a story arc to that as well the episodes can also be enjoyed as stand alone adventures too.
Then with the Shorts/Sketches these I would say seeing after a few NPLH episodes really to get the most out of the 4th wall breaking antics and understanding the relationship between Holmes and Watson as played by Myself and Mike Archer.