Regardless of camera brand, I always recommend this site for learning how Aperture, Shutter Speed, and ISO will affect your photos -
http://www.canonoutsideofauto.ca. It has a learning portion and simulation portion that lets you virtually take pictures in manual mode, adjusting each setting to see how it affects the results - Motion blur, depth of field, and noise. In regards to focusing speed, it's a combination of both the body and the lens. Some of the cheaper lenses are just dog slow focusing regardless of how good the AF system is in the body.
I myself moved from a Canon DSLR (7D) to a Fuji Mirrorless (X-T1) a few years ago because I got tired of packing all the heavy DSLR gear around for travel and vacation. Fast glass for DSLR's is VERY heavy. I would only recommend a DSLR nowadays if your sole intention is to shoot field sports, or if you have some other need for a long fast prime. I recently picked up another used Canon 7D and used 300 F/4 IS L as our oldest made JV soccer and I needed the extra reach. A 300 F/4 isn't really considered fast, but was fast enough for our late afternoon outdoor games. The Fuji 100-400 lens would have set me back $1900 new. I have less than $1k invested in the 7D + 300 F/4 combo. Which brings me to another 2 points...
1) Bodies come and go, Good glass lasts forever
The resell value of bodies drop like rocks. Good "professional" glass however holds its value for years as long as you take care of it. I've bought lenses, use them for 3 years, and sold them for more than what I paid. And these were even new, just picked up with good discounts. But this brings me to the 2nd point...
2) Buy used!!!
Whenever a 2nd generation body comes out, the previous generation body will flood the market. Take for instance the Fuji X-T2. It's $1600 new for the body alone. Fuji currently has a $500 rebate on the X-T1 now dropping it to $800. I've seen tons of X-T1's on the used market for ~$600 that aren't moving!! Once they drop below that point however, they sell quickly. Point being, don't be afraid to buy used from someone with a good rep, like the people on Fred Miranda -
http://www.fredmiranda.com/forum/board/10. That's where I recently scored the killer deals on my 7D and 300 F/4.
With all that being said, my recommendation would be a Fuji X-T1, the 18-55 lens (included in kits), XF35/1.4, and two extra 3rd party batteries from Amazon. All used, except for the extra batteries. You should come in under $1200 if you shop around. With Fuji, you'll find all of the XF lenses are very well built and quality glass, unlike many of the cheaper "kit" lenses that Canon and Nikon include. The former's kit lenses are nothing at all like the stellar 18-55 that Fuji includes with its kits. Again, this is all coming a X-T1 user who loves his camera. I plan on upgrading to a X-T2 once the used market starts to drop a little, so it'll be a while. The 35/1.4 is a beautiful lens, albeit a little slow on the focusing side. The Rokinon 12/2 is a cheap and fast ultra wide if you don't mind manual focusing, which is pretty easy to do it on ultra wide lenses. The Fuji 10-24/4 is a stellar lens, however is much pricier.
Whichever route / brand you decide, research it, then research the used market.
Here are some Disney and Universal Flickr Albums all done with the X-T1:
Disney 2014 -
https://www.flickr.com/photos/sporadic/albums/72157651121895628
Disney 2015 -
https://www.flickr.com/photos/sporadic/albums/72157654515140332
Universal -
https://www.flickr.com/photos/sporadic/albums/72157668565432950
10-24/4:
Rolling through Big Thunder by
smerrick, on Flickr
35/1.4:
DSCF2214 by
smerrick, on Flickr
35/1.4:
Makeup time by
smerrick, on Flickr
35/1.4:
Kitty Cat Princess by
smerrick, on Flickr
35/1.4:
DSCF2291 by
smerrick, on Flickr
35/1.4:
Relaxing in Germany by
smerrick, on Flickr
35/1.4:
DSCF2374 by
smerrick, on Flickr
35/1.4:
Reign of Kong by
smerrick, on Flickr
10-24/4:
Gringott's Dragon by
smerrick, on Flickr
And some recc league soccer shots with the XF 55-200:
DSCF4583 by
smerrick, on Flickr
DSCF4445 by
smerrick, on Flickr
DSCF4406 by
smerrick, on Flickr