How many strings should your harp have?

When you start researching harps, one of the first questions is "how many strings do you need"?
I recommend that you first rent a harp to get comfortable with the instrument and understand what you need from your harp.  A beginner can get plenty of work done on a small harp (<32 strings).  A small harp is also ideal for travelling.  Some examples of small harps:

​Dusty Strings Ravenna 26
Salvi Juno 25 or 27
Fullsicle 26

If given the choice between a lap harp and a floor harp as your main harp, opt for the floor harp.  The positioning is more comfortable and it will be an easier transition to a larger harp later.  

As you reach the advanced-beginner/intermediate stage, you may find that the smaller harp is too limiting.  Larger harps offer a rich bass and more resonant tone.  An instrument in the 33-40 range is appropriate for most harpists.  Personally, I think 34 or 36 string harps have the best value.  My main harp is a Salvi Livia 36 string harp (discontinued).  A 36-string harp will go from a C2-C7 whereas other harps will add/remove a few strings from either the top or the bottom range, for example C2 to A6.  Remember, as the number of strings  increases, so will its size, weight and price.  There are many brands and models to choose from so take your time to research and try as many harps as you can!  Here are some suggestions:

Lyon & Healy Ogden - 34 Strings
Dusty Strings Ravenna - 34 Strings
Josephus Moonspring (Made in Canada!) - 36 Strings
Salvi Titan - 38 Strings
Lyon & Healy Prelude - 40 Strings

TLDR: Rent an instrument as a beginner and invest in a 34 or 36 string harp .  It offers flexibility without being too large.