Is it up to me?

[Naberrie]

So if I combine an archer with an conjurer I will be less likely to be chosen as a partymember for dungeons?

The thing is that any skill you could take from Archer to use on CNJ would be useless in a party. You want to take skills that are useful. Skills like Swiftcast from Thaumaturge, or Eye For An Eye from Arcanist are useful. Raging Strikes and Hawk's Eye are not. Not for a CNJ.

When you solo you can do whatever you want, but when you party remember that everyone else needs you to perform a certain roll. If your damage dealers showed up with Cure from CNJ and didn't do any damage but just spammed Cure, you wouldn't get far. If you show up popping Raging Strikes from Archer and Internal Release from Pugilist, not only will they be no help to you, but your party will probably end up dead.

[Elysaine]

I only have 3 classes at the moment. Whitemage (Conjurer), Arcanist and Thaumaturge. Even if I had other classes already, I would only use cross class skills from these three classes. Because they benefit a caster class the most. My guess is if you solo on Archer and have Cure as backup spell it might help you out of a bind. But don't expect to be using it in a dungeon. As Archer you're a dps class, not a healer. So you wish to have abilities from other classes which will improve your DPS It's the other way around for a healer

Only DPS improving skill I've picked up on my Whitemage/Conjurer is the Thaumaturge's Thunder. It's a DoT spell. Increases your damage a bit, and I have never been frowned upon for using it next to Aero in a dungeon. Just to add some damage when not being required to heal at a moment

[Merryl]

I believe what your looking for is this http://www.ffxivguild.com/ff14-job-requirements-arr/
On that page you will find links to the classes that share cross skills and the job titles associated with them.
For archer your best choices would be THM for black mage, or if you want to keep archer skills on top chose pugilist for bard. Lancer also crosses with pugilist for dragoon.