Pay attention to your cards. Most beginners only look at the skills they give, but the most important thing are the passives on the cards. Look specifically for training bonuses, then yuujo/yaruki bonuses. All the top level cards have 2 or 3 of them at a high percentage. Then you want to see how much hp recovering events the cards have. You always want to select the event (if there is a choice) that recovers your hp because the stats you can get from training is always better than what the event gives you.
Pick your inheritance carefully. For now you won't have good ones to use on your own, but rental something good. Preferably with 9 blue (high on stam) and at least 5 URA/aoharu scenario. You can min-max on skills after you get a 9 blue of your own.
Remember that the URA final's distance and field will be equal to whatever most races you did in that run. For example, Bourbon has 3 mile, 3 mid, 3 long as her required races. If you do one more, say takarazuka kinen, that brings mid to 4 and URA final will be mid. If you don't do anymore, the tiebreaker will always choose the shorter distance so URA final will be mile.
For your skills, try not to get any as much as you can. It is always worth it to play with 0 skills and learn them all at the end as you wait for more hints or kiremono.
Finally, HP management. As I mentioned earlier, you want to recover HP as much as you can by the event cards. You can also use int cards (fine motion, nice nature, curren chan) to recover a few, but that's usually for nige horses. Bring a lv 50 trainer card (tazuna for URA, riko for aoharu) and use it to heal whenever you can. Check a wiki for stats and event of all your cards and horse-specific events if you don't have the memorized yet.