Skills highly depend on the situation, f.e. in PVP it's all about fast skills, ideally stuff you can use each or every second turn. Most common setups here are a healer, brown card generator (change all x cards to brown recovery cards), defense buff, direct damagers or vampire skills (inflict x damage and restore same amount of HP) and wild card generators/9+2 if you can pull that off without too much def/HP loss.
PVE is really situational, a tower team requires a different setup than some event islands.
While you ideally still want your skills as fast as possible, there's some slower skills that can be useful in PVE such as delayers (adds x delay to enemy) and reducers (reduces the number of turns before a skill is active).
And again, 9+2 or wild card generation is what you usually want to aim for here.
x chance to kill an enemy skills are useful in tower, not sure if anywhere else really.
Then there's also mono teams, where you want something to reliably generate cards of the respective color.
Mono teams can also get some huge buffs since race-specific buffs (check out Zhuqiaomons skillset on the current top left event island to get an idea) stack with generic buffs (f.e. small def increase of all allies), while neither two generic buffs or race-specific buffs of the same type would stack.
This got really long already and i'm sure i still forgot to mention lots of good skills. In general, i'd just keep all SP and higher mons, for lower stuff check the wiki if they evolve into anything interesting, if not it's most likely food. Some God+ mons like Bellestarmon, Beelzebumon, Daipenmon or Phelesmon are temporarily worth to keep until you have something better with the same skills.
There's also a few "stat-stick" mons like Craniummon SP or Raidenmon, which can provide a huge amount of defense if your team is overall still lacking that. Especially Craniummon is worth it and easy to make, drops at Imperialdramon PM island in Aegiomon trials and needs only one evolution.
About Examon, he's so-so. His skillset is not bad, but the more interesting +9 gets heavily slowed down by his other skill, and takes up the leader spot. Since you've got Bellestarmon already, just keep using her for +9.
Lucemon Larva is indeed only really needed for higher tier PVP, but it doesn't hurt to keep working on him already as you will (or should) get to this point eventually. PVP is imo pretty essential to gain access to a weekly Burst Cap, and a good amount of gold disks and some other stuff.
Edit: Forgot to mention, Limit Breaks will also reduce the turns needed at either 1-3-5 or 2-4 depending on the digimon. Here's a somewhat outdated, but still useful list: http://forum.digimon-heroes.com/t/guide-about-skill-turn-reduction-when-limitbreak/2008