Horse racing fanatic here. The Triple Crown (esp the Derby) is my Super Bowl. The Derby is the longest running 'sporting' event in the US, so there is a lot of history and idiosyncrasies to the race. I will preface by stating that I cannot help you with the betting aspect of it, as I am not a gambler by any measure, however, I will try and fit in two plus decades of following horse racing into this condensed post:
Three races make up the Triple Crown for the best crop of 3 year olds, beginning with the Derby the first Saturday in May, then to the Preakness (Baltimore) two weeks after and the shortest of the three, then three weeks after the running of the Preakness is the Belmont in NY the longest of the three. (The Great Sandy has claimed the hopes of many great Triple Crown hopefuls.) Then the largest purse in North America is the Breeder's Cup Classic run during football season (so it doesn't get too much coverage but the winner gets a nice $5 million boost and bragging rights.)
Specifically relating to the Derby, the main race is the very last, but there are many undercard races of general interest run throughout the day. The Kentucky Oaks is run on the Friday before the Derby and is reserved for the best crop of 3 year old fillies. (Songbird was blazing through toward a Oaks win last year, however, she was pulled because of an illness.)
Typically one can gauge some early-on favorites by the graded stakes run to qualify for the Derby. They recently (two years ago, if memory serves right) changed the point system, but either way, look for the Juvenile Breeder's champ to be the early favorite coming into the new season. Last year's champion was Classic Empire out of Pioneerof The Nile (also studding the last Triple Crown Winner, American Pharoah). He can be a bit rank, but has the talent. The horse making a ton of noise out of the Florida Derby is Always Dreaming who logged a time that was comparable to the great Alydar, a colt from the famed and troubled Calumet Farms. (Side note: Alydar was the only horse to finish 2nd in all three Triple Crown races to the great Affirmed.) With that being said, the track for the FL Derby has had some trouble with time keeping, so many in the racing world is quite suspicious of the official time. Then there is Irish War Cry (name alone is enough for me) but he is out of the great Curlin whose earnings won him the title of the winningest North American racehorse, and was only surpassed by the lovable California Chrome only last year.
One should not rest upon the laurels of previous races. There are a great amount of variables and come with each race. Gate position is a huge factor. Breaking from gate 20 or 1 in a 20 horse field (the size of the typical Derby field barring scratches and such which is a problem in and of itself) puts the horse in a great disadvantage. (The ideal is 5-15.) If your favorite pony draws post 17, good luck. No horse has ever won from that post.
People tend to gauge a horse by its trainer as well. Baffert has been dominate of late. However, his best bet this year, Mastery, was pulled from Derby talk after sustaining a none life threatening injury this spring. Todd Pletcher is always a one to keep an eye on, and also Desormeaux is making a name for himself.
Churchill Downs itself doesn't quite seat all 130K+, they permit attendance in the infield. As for the boxes, well, there are a few areas unabashedly called 'Millions Row', tickets are definitely hard to come by and the airport is always filled with private jets. (Think the scene of when the Horns traveled to Ole Miss.) But it is a place to be seen, no doubt. The grounds of Churchill Downs has the placard with all the past Derby winners hung along the perimeter of the main building, with the Triple Crown winners' names in yellow instead of standard white.
The food associated with the Derby is of course the Hot Brown sandwich named after the fantastic Brown Hotel. (Certainly worth the visit, and then head to the Seelbach Hotel down the way, a haunt of famous folks from Al Capone to F. Scott Fitzgerald.)
Derby hats and bowties are of course the standard, but if you ever want to check out something even more incredible, try out the Ascot run in England. Do they take it over the top.
There have been a few great fillies in the past decade or so to run in one of the Triple Crown races: the tragic 8 Belles (who lost her life after placing against Big Brown) and of course Oaks winner Rachel Alexandra who jockey Calvin Borel chose to ride over Derby winner Mine that Bird in the Preakness. (Still my thought that if Borel rode Mine that Bird, the Triple Crown drought would have be ended that year.)
The variables are incredible to have any shot to even qualify for the Derby, but the race itself is full of intrigue that at times things can go wrong for the favorite and things can go right for a 91-1 underdog (Donerail, 1913). It is so much fun to place your hopes on a horse and go from there.
Hope this post helps a little.
