On a camera with a 1.6x crop factor, like yours, or my 7D and 40D cameras, I like a fast 35mm for children, pets, and family at indoors distances, and nothing in the Canon line beats the 35mm 1.4L.
First, however, know that the 50mm is a truly good focal length, and you can learn much by learning to use it well, alone, first. A good flash unit, or flashgun, if used well, should be considered. I was very lucky to have the use of a 580EX from the start of my DSLR shooting, though it took a while to learn to use it well. How I do wish I had started with Syl Arena's truly excellent book on the subject of Canon Speedlites! (It was not yet available at the time.) Amazon.com has it, and if you follow the link from Cameralabs to the Amazon site, the purchase will cost you nothing extra, but Cameralabs.com will benefit financially.
Yes, I do recommend starting with the relatively expensive 580EX II, based on your stated budget. This powerful flashgun can cover amazing distances,
but the light can be directed/modified to be as soft and diffused as you want. Something as simple as a white ceiling is a wonderful modifier! A shoot-through umbrella is good purpose- built modifier.
Then, with one, or even two good flashguns, look into a high-quality zoom
lens. I almost immediately invested several prime (fixed-focal-length) lenses, so actually have no experience with the L zoom lenses, so I will defer to
others' experience in that regard. The only zoom I regularly use is the truly wonderful 10-22mm EF-S, but ultra-wide lenses are an acquired taste, so might not be good at the start.
Edited to addFor what it is worth, as I manage to do the majority of my shooting with the 35mm 1.4L, 100mm 2.8L Macro, and the 10-22mm EF-S, if I could only own three, for a cropped-frame-sensor camera, these would be my choices, though a 50mm could substitute for the 35mm fairly well.
Canon 7D/5D/40D/1D2N; Nikon F6, D700, FM3A, & Coolpix A; Canon 40mm 2.8 STM, 135L, 50L, 35L, 50mm 1.8 I, 100mm 2.8L Macro, 10-22mm EF-S, 28-135 EF, 400mm 5.6L; Nikkor 50mm 1.2 AI-S, 50mm 1.4G, 50mm 1.8D, 16mm 2.8D Fisheye, 180mm 2.8D, 100-300mm 5.6 AI-S, 18mm 2.8D, Voigtlander 90mm f/3.5 SL II