Avoid using Titania. She will kill enemies easily for a while, but she'll grow extremely slowly. If she's hogging all the experience your other characters won't get any stronger so you will struggle. The best thing to do with her early on is to take away her weapons and use her to bait enemies for your other units to kill. Or give her a very weak weapon and have her weaken enemies for someone else to finish off.
The Laguz in PoR/RD suck, don't use them.
Don't promote your units until level 20, since promoted units (like Titania) gain experience more slowly. Ike is an exception, traditionally the main character automatically promotes at a certain point in the story and he does after chapter
(spoiler in case you don't want to know). So you should try to have him at level 20 at that point if possible.
Beating chapters more quickly and accomplishing certain unlisted objectives (like not letting NPCs die, for example) gets you more bonus experience. You can't use it in the first few chapters, but once you get the pre-battle menu you can use that to divvy out experience before a chapter. Bonus exp is pretty valuable since most Fire Emblem games don't really allow for any sort of effective grinding, you just have to go with what you have.
Regarding the difficulty, I don't remember it ever spiking. It's a pretty reasonable difficulty curve with just a few bumps.
And sometimes you need certain characters to recruit others. Many can be recruited just by talking to them with the main character (Ike in this case) but some have relationships with other characters. There are usually hints about this in the story dialogue or pre-battle discussions. Most (but not all) non-boss enemies with character portraits can be recruited, so keep that in mind.