There are many threads on this subject. This is a good one, with lots to read.
As far as finding horses with pedigrees you like: studying CANTER is a great idea. It develops your eye for horses you like-- and then look up the pedigree and try to find common ancestors. After viewing many, many horses you’ll get good at identifying certain features and where they came from (the Storm Cat type, the Pleasant Colony type, the Fappiano type, etc) and how they blend.
If you’re interested in a specific sire/dam, you can do a progeny search on Pedigreequery.com. It may not be 100% accurate, but it’s a good (free) start. Perhaps it will lead you to photos of other offspring, or at least identify individuals and allow you to look up their race replays.
Here’s my response on the forementioned topic, copied here:
While I love all these old names mentioned, it’s getting harder and harder to find them up close. And one thing I remember from a very grueling Genetics class in college is that past the 4th generation, it’s so dilute that it probably doesn’t matter.
-Parents 50/50
-Grandparents each 25%
-Great Grandparents each 12.5%
-Great great Grandparents each 6.25%. (Meaning 93.75% of the genetics likely comes from somewhere else.)
Now, there are prepotent lines, which may trend down a long ways. But seeing one name waaaay back there means very little to me, statistically.
I’m finding myself studying “current” sires and lines a lot more, trying to pick out trends and the ones who produce what I like. Fortunately, being in Lexington and working on TB farms for a few years let me see a lot.
Of more recent sires, I like:
Pleasant Colony-- tend to be long-legged, uphill, big gallopers and above-average movers. Knew one personally who did very well in YEH and evented to intermediate.
AP Indy-- gosh the good ones are so athletic. The ones I’ve known had good minds, too. It helps that AP Indy saw a lot of really nice mares, so you’re not likely to see many duds. 
He has quite a few sons at stud, and some are more successful than others, but it’s a bit early to tell which exactly will make good sport horses…but I’m optimistic. I have an AP Indy grandson who greatly resembles API moreso than his sire; this isn’t uncommon, in my experience.
Pulpit, by AP Indy-- they seem to be stamped with nice front ends, beautiful arched necks and shoulders. Some of them are kinda short with chunky pony bodies, but those with legs are super nice…and most of them are athletic, chunky or not.
Langfuhr-- usually have big, huge shoulders, big hips, and an enormous walk. If they aren’t too big for themselves, pretty nice movers and jumpers.
Fappiano and his relateds-- it’s hard to go wrong with Fapp relatives: Quiet American, Comet Shine, Unbridled, etc. Unbridled’s Song himself gives me pause, but the rest of them make me happy. All seem to have great proportions, nice toplines, good solid horses and overwhelming success in sport.
Sadler’s Wells-- he’s made a tremendous amount of nice turf horses, and some super jumpers too. I’m a fan of his son El Prado, too…usually pretty proportionate. And another who makes yummy-looking kids: Medaglia D’Oro, by El Prado.
Storm Cat-- yeah they can be headcases, but also athletic, cat-like, and some are great movers. I’m not crazy about most SC sons at stud…I run away from Giant’s Causeway, for example, but it depends on the horse. I’ve liked a few Hennessy’s-- but I love Hennessy’s dam (by Hawaii). SC on the mare side is highly variable…some are nice, some are not, hard to judge.
Roberto-- not always the best movers, but great jumpers. Rode a Roberto foxhunter who was as game as they come. Roberto seems to be fairly common among steeplechasers (like McDynamo, by Dynaformer, a son of Roberto).
Others I’m keeping an eye on:
Include-- by Broad Brush, he has some old school up close. I’ve only seen a couple personally, but they were tall, uphill, long legs and big flowing strides. My type.
Empire Maker-- it sucks he went to Japan, he’s had some nice athletic types. Don’t know many in sport horse careers (yet), but I like the type of horse he makes: moderate size, proportionate, classic TBs with big hearts.
Tiznow-- he stamps his get well with a super classic TB look. They always seem to catch my eye out in the field, just the way they’re put together: long legs, long uphill necks, with a look of eagles. Tend to have upright pasterns; don’t know how well they hold up, or if they jump, but I’d be willing to give it a try!
Lion Heart-- he himself was decidedly NOT my type, but I fell in love with quite a few of his offspring who were well-proportioned, leggy, and had great minds. Good-looking horses, too bad Lion Heart went to Turkey.
Cherokee Run (and sons)-- I haven’t met enough of them personally to get a good judgment, but they tend to be light, athletic types with chrome. I get the impression they’d jump the moon and move well, but don’t know enough of them in sport to say for sure.
