I hand stitch using a sharpened awl and 5 cord twisted sinew thread, generally following what is prescribed in Al Stohlman's book "The Art of Hand Sewing Leather". I highly recommend this due to its relatively low cost and array of information on how to stitch items from buckles, bags, baseballs, etc.
Harness needles actually come in many more sizes than three. CS Osborne makes them in 10 different sizes. I think I generally use a size 1. Harness needles have a rounded tip and are not sharp, intended to be used with an awl or preformed hole.
Small needles sound nice but I like larger ones because they are less stressful on my fingers and I can apply more force, before having to resort to using pliers. Just make sure the thread you are using will fit in the eye of the needle. Tapering the thread (and eye glasses

) can help.
Most people use synthetic threads today which have some arguable advantages due to strength, but I have enjoyed using Barbour's Pure Flax Sinew size 5 left hand twist strand. This thread is white but can be dyed before or after stitching. I bought my 1094-yard roll at Campbell Bosworth Machinery probably 15 years ago, and am no where close to thinking about when it will need to be replaced.
The CS Osborne harness needle specification page is
HERE. I'd suggest size 1 through size 3.
HERE'S a good location to buy natural sinew thread. If you are interested.
Mike