This can get really complex, and, as you imagined, very expensive.  There is this sudden realization that good scopes are pricey, and the less expensive ones are, well, to be honest, not worth the cash. They end up in closets or basements.  For a first time telescope, especially for kids, I always recommend a really good pair of 8×50 or 10×60 binoculars. These get good use at night, AND during the day… bird, scenic views and the like.  If we are talking seriously into astronomy and telescope are the only choice, then go for the most scope you can afford: one with a quality heavy mount and large aperture.  My close friend Ed Ting has made a wonderful page with a load of buying tips here:  http://scopereviews.com/begin.html Do start there and work through it.  At all costs avoid the department store telescopes. They are a plague in our science with their cheap, shaky mounts and promises of ridiculously high powers 😉

Coupled with a telescope purchase is the inevitable need for some accessories. I’ll list a few here to consider:

• A wide range of good eyepieces. These get expensive but will last a very long time. I recommend three to start, one for low, medium and high magnification. Magnification can be found by dividing the telescope’s focal length by the focal length of the eyepiece. Typical low power magnifications are on the order of 25-30x.  Medium: 75-150x. High: 200-300x. One rarely uses the high magnification. Honest!
• A good sky atlas. Good ones can be used for eyes, binoculars and small telescopes like these options: Sky & Telescope’s Pocket Sky Atlas – Jumbo Edition and the Sky & Telescope’s Pocket Sky Atlas.
• A red-light flashlight. A simple regular flashlight with red cellophane covering is good.
• Maybe even a subscription to Sky & Telescope Magazine or Astronomy Magazine. These help the newcomer by projecting what good targets will be available in future months.

Stay well and enjoy clear skies!