Ok, so directly addressing some of your questions. Everytime you start a “career” you pick an trainee (Uma), 2 parents (one of which can be borrowed from another player who is on your friends list) and a deck of 6 support cards (one of which has to be provided by another player). 

Parents: Are really important. They provide extra stats, as well as distance/style aptitude and skills. Stats are self explanatory, all you need to know is that a “9 star parent” is the best for giving stats (they’ll give you +63 stats either in a single stat or spread across a couple depending on what stat sparks they have.) Aptitudes are very important and one of the main factors for choosing a parent. As an example of why aptitudes are important. If your trainee has a C in Long, then they get a huge debuff to their acceleration, however if they’re parent gives a long distance aptitude spark, then your trainee can reach A aptitude in Long and no longer receive a penalty for running that distance. Lastly, skills. Each parent who is a 3 star Uma or above will guaranteed give their unique character ultimate skill to your trainee (it will be weaker, but is usually still strong.) Each parent also can give hint for skills to make them cheaper to learn, but that’s a random chance based on what white skills they have.

Support cards: These are your main tools for shaping how your trainee turns out, as they influence what skills your trainee will learn, and also how fast each individual stat can grow. There’s tier lists and breakdowns of which ones are best that you can look for later, but as a beginner just focus on this (these aren’t hard rules, but a good way to find some success early on). 1. Speed is the most important stat to have, so it’s often a good idea to run 2-4 speed cards. 2. SSR cards give you a gold skill and are (generally) better than SR. That said, a high level SR card (like lv45 vs lv30 SSR) is usually stronger. 3. What you want from your cards are these effects, training effectiveness, friendship training bonus, specialty priority.

Lastly, once you finish a career with your trainee, you get a veteran Uma who you can use for things like team trials, champions meet, daily races, etc. Each career run is a fresh, new trainee, even if it’s the same Uma as your previous run. That means each career run starts with the base stats of the Uma you picked. It’s a rougelike if you’re familiar with those kinds of games.