If you are on a budget, and a student learning photography, I would recommend going the prime route.
I very much disagree.
For one, a single zoom is cheaper than a trio of primes covering the same focal length range.
For another, primes are specialized tools. The only time you want a prime instead of a zoom is when the prime does something the zoom doesn't.
It used to be that that meant image quality, but no more. Many of the lenses with the best image quality are zooms, and some of the lenses with the worst image quality are primes in popular focal lengths. For example, the 20mm f/2.8 -- a perfect medium-wide for APS-C, is one of the most "meh" lenses in Canon's lineup. And the worst lens I've ever owned is a Canon 28 f/2.8, which should
be the ultimate normal lens for the format.
It also used to be that that meant speed, but not very much any more. While there are times when you want to shoot faster than f/2.8, those situations are rare and marginal. With the high ISO capabilities of modern DSLRs, you don't need the speed for low light shooting. And razor-thin depth of field effects are a specialist "look" of a certain style of portrait photography.
Now, there are a number of specialist lenses that happen to be primes that are well worthy of consideration. True macro lenses are always primes, for example, and lenses with movements (TS-E) are always primes. Until the 200-400 goes on the market, all the Great Whites are primes. The amazingly diminutive Shorty McForty is a prime. And, yes, the super-fast portrait lenses are all primes.
But each of those lenses has something in particular that it does that a zoom doesn't, and it's for that something in particular that you'd want said lens. When you don't need that something particular, though, the zoom is far
superior to the prime, as it's literally a bag full of primes in a single lens for less money.
Some will suggest that the big limitation of a prime -- that you can't change focal length -- is somehow a creative advantage. Bullshit -- with a simple piece of gaffer's tape, your zoom suddenly acquires the exact same creative advantage as the prime. And a two-second adjustment gives your zoom the same advantage as with another prime of a different focal length.
So, rattlit, my suggestion still stands: get the 17-55 (and, if you really think you need it, a $2 roll of gaffer's tape).