What to look for when buying a digital piano/keyboard:

Suggested features to look for in your beginning instrument -

Full-Size Keys - Keys are the width of real piano keys.
Touch-Sensitive Keys - Keys sound soft when pressed lightly and sound loud when pressed hard.
Music Rack - Holds up the music book
Built-In Speakers - Keyboards and digital pianos should have built-in speakers; synthesizers will not.
Damper Pedal Jack - Quality pedal is usually sold separately.
“True Piano Sound” or “Grand Piano Sound” 
Weighted Keys - Feels like you are pressing down a real wooden piano key instead of a light piece of plastic.
88-Keys - The more keys, the longer a student will be able to use it. A digital piano/keyboard with 88-keys is the same size as an acoustic piano.
Not very many extras - Many digital pianos/keyboards come with features that you don’t need - 500 instrument sounds, 300 prerecorded songs, etc. Spending your money on the quality of the instrument rather than the quantity of extras is recommended.
Yamaha/Casio - I prefer Yamaha as they are well made, sound good, and have worked well here at the studio.   

Here are some suggested models:

Yamaha Arius Series (YDP-xxx)

Yamaha P125

Yamaha P45 (Amazon's P71 is a comparative model)

Casio Privia Series (PX-xxx)

Here are models with less than 88 keys for tighter budgets:

Yamaha NP32 76-Key Piaggero  (Buy power adaptor separately)

Yamaha NP12 61-Key Piaggero  (Buy power adaptor separately)

Links to helpful articles and videos:

Hoffman Academy article - Choosing a Piano or Keyboard for the Beginning Student>> 

Kraft Music video - How to choose a digital piano>>

If you are in the market for an acoustic piano (grand, upright, studio, etc.):

Lepinski Piano website - Las Cruces - worth the drive>>

These suggestions are my personal opinion only, not an endorsement.  The store/vendor where you buy your beginning instrument will be able to help you decide what is best for your particular situation.