http://www.ffxivguild.com/ffxiv-bard...-skills-guide/
That's a decent guide for cross class skills. I recommend going for pugilist level 12 first and the get lancer at your own pace. Invigorate and Blood for Blood are useful but it's not going to hurt your leveling much to not have them.

As for professions, I'd say start the ones you're interested in immediately so your bags don't end up full of materials from mobs. You can level all crafting classes to about 15 with just vendor materials, and gathering is quite fast aswell. A good pairing is mining and goldsmithing, because goldsmithing isn't very dependent on other crafting professions. Also with goldsmithing you can make jewelry for every class. Right hand side gear is quite hard to come by when leveling your battle classes.

Here is more info about the DoH and DoL class dependencies:
http://eorzeareborn.com/crafting-and...-realm-reborn/