What to look for in wood selection when building a coffee table frame with glass top
Knowing if the wood is appropriate depends on a lot of factors, but if you're building something close to what's in the photo you might want to consider Beech (good indoor furniture wood). White Ash has more grain and color to it. Poplar can also work (and may be more readily available in local DIY/big box stores). It will depend somewhat on your locale to build something from what's readily available and suitable for the climate. 

There's nothing overly complex with the coffee table as pictured. You will want to think about the joinery methods for the various pieces of the frame to be stable and rigid.