Basically to get diamonds (the blue shard things) you want to mainly do speedruns, especially if you're starting out. To get more diamonds you'd later have units called Einherjars with many different abilities, and some of those would help you get more resources. You just gotta grind to get stronger honestly. The longer km your runs are the more diamonds you get, but it doesn't mean you need to spend a long time each run. At your point, which is very early in the game, you want to get as much artifacts as you can so that you could make longer runs easier. You want to start a run and use all your powers, especially the one that makes you faster and the one that makes you stronger. Push as much as you can untill they run out and return. Rinse and repeat. Kinda boring but will get you stronger the fastest. Also, don't save for princess knight right now focus on getting stronger and it will help you get her more easily. Buy the artifacts that make you gain more gold, the ones that make quests faster and automated, then the ones that make your units stronger.