Starting out you will have 0 money.
Raising your first Digimon
The only egg that is free is an egg that will hatch into Botamon and then Koromon. After reaching the Koromon stage the next Divolution will depend on how well the Digimon's needs were met while growing and its battle record. A certain amount of battle wins are required to reach some of the farther Digivolution stages.
Overall care
Overall care of your digimon depends on how you wish to digivolve it.It involves feeding,training,and optional extra feeding items that raise speed and stamina.
Earning to advance
To make money for items and better eggs you must win battles against other Digimon. In the game's main menu there are 3 options that say Data, Virus, and Vaccine. You can fight computer controlled Digimon of these types by selecting these options. If the Digimon that are sent out win you will win money. Wait until some of your Digimon have reached Rookie or Champion stage before fighting here. Going in with more than 1 Digimon can also give you an advantage.