I can tell you guys a couple of conclusive tips from watching Japanese guides, and just from experience.
You want 2-3 highly rated SSR or SR cards for speed, endurance, stamina, and wits. The only training card you care about is the tutorial girl, the one with green clothes. This is one of the support card that you can borrow, so dont bother rerolling for it. Keep in mind, the cards needed differs on the unit that you use so dont generalize that you always need 3 speed cards for every horse girls. Some horse girls do need 3 stamina, some need 3 speed, and so on. But we know for sure that guts support card is universally terrible. Guts is basically the one with the flame icon.
This means you have to priotize support cards not characters. When you do your gacha, make sure to do support cards and get the right deck first, then summon for characters. A character is useless without good support cards.
There are 5 training routines that you could do. Depending on the meters or the type of race that you're doing, you will either need more blue skills if you have below than average stamina but a lot of speed and endurance; or, if you have above than average stamina, endurance, or wits, yellow skills are the token to victory in place of speed. Even so, having high raw speed is always nice.
Speed > Endurance > Wits (skill activation rate) > Stamina > Guts (increase speed midpoint of the race). You should priotize your stats by that order. 4 and 5 can be skipped entirely. Unless you're doing like a 1800+ long race, stamina at 300-500 is a good range. If you have too much stamina for short races, it's kinda like having 5 chances to hit a ball, but the challenge was to hit the ball once, the other 4 chances are seen as a wasted stat.
Simply put, just train mostly speed, endurance, and wits. Raising endurance can indirectly increase your stamina so dont bother too much on doing the stamina training and only do a few of them, unless you're doing the long races.
There will be an option to check your status, whether it meets the requirement for the race or not, before you start your race. This represents in "O", "X", and a triangle symbol. O = you have enough, double O for exceeding the race's requirement (you dont want this on stamina), X = you know what, triangle = you're between O and X, barely passing.
And that will be it, have fun everyone. You can find deck guides online if you cant clear the entire tournament. It's rough but not impossible without it. Search for your horse girl and what deck they used for her. Also, skill order is another important factor to getting every 1st place in each race, but you should really just have fun and play around with what you got.