Well these features are up to you but from my hazy memory of the tv series (which you'll probably want to follow considering its a fangame) they only ever had one digimon each right? so that rules out catching, and how many to have in a party.
Also they only ever digivolved for a fight (though I'm not sure since sometimes they seemed to regress to earlier stages? either way they never stayed in powerful forms longer than a fight) so that could be a cool little transform system in battle.
In regards to story heres a tutorial on fangames; http://www.rpgrevolution.com/forums/index....showtopic=54913
but ultimately its up to you how you want it to go
Also theres a tutorial for egg hatching similar to a previous digimon game here http://www.rpgrevolution.com/tutorial/how-to-make-
Edit: that bottom link wont work because theres '[ ]' in the title, you're just gna have to look through the tutorials yourself if you're still interested