I guess the whole "baron, count, duke, king, emperor" thing isn't exactly easy to understand for first time players. Same for the tile systems, the different types of claims and the "auto-military access" thingy ("OMG why are there armies in my territory?!").
When you start (and, well, afterwards as well), all you really need to understand about the title system is which rank outranks which, since the main purpose of ranks is to allow you to vassalise - you can only vassalise ranks below yours (and I still get caught out by this, awarding duchies to people only to have them become independent. I start as Wessex, a petty kingdom, and a petty king = a duke).
Higher ranks can also hold more personal territory, so it's good to be able to create a new, higher title for yourself when possible (though once you hit Emperor there's no particular benefit other than sandboxing to holding extra territory - you get extra vassal armies, but the core territory of most empires gives you all the military you really need).
The different types of claims is something shared with EU IV, I think? For the most part a claim is a claim and the rest is flavour - the difficult thing to grasp (and I still don't completely) is what you need to do to place yourself to inherit a claim, since the succession system is rather arcane and it's difficult to trace who counts as a sufficiently close family member to give you a claim or inherit as a vassal (grandchildren don't seem to, for instance).
Commonly early in the game, you'll only be able to claim by:
(a) having a de jure title that contains land you don't own (for instance, if you form the Kingdom of England as Wessex, you can press claims for any English territory you don't own)
(b) fabricating a claim
(c) sharing a border with an infidel or pagan (allowing you to claim the neighbouring territory through Holy War), and:
(d) inheritance - this is ultimately the most important type of claim, but also the hardest to get to grips with. The earliest way you'll get a claim this way is by marrying someone with a claim, but pressing on your wife's behalf won't give you possession - having a son, pressing the claim on your wife's behalf, and then arranging for her to die conveniently soon afterwards is the surest way to get this land, but you have to be aware of the succession laws for that particular territory: I tried this approach with Aquitaine in one game, unfortunately Aquitaine had seniority succession so the territory wasn't inherited by our son.
At least in the early game I'd try marrying people with claims to keep the claims in the family, but not pressing them until they're due to expire a couple of generations later. By that time you'll hopefully have a better understanding of how the system works, since once you're into it it starts to become fairly intuitive as, like any Paradox game, there's a lot of rinse-and-repeat gameplay mechanically.
Armies in your territory are only something to worry about if they're red - and no, you can't shut them out or close borders. CK II is all about politics, but its diplomacy system is extremely limited and rudimentary - basically you can give people stuff for favours (i.e. improved influence), but that's pretty much it. You can't arrange treaties of any kind (alliances are something else linked to the dynasty system, and again are rather arbitrary in terms of who counts and who doesn't - in-laws of close family members count, grandchildren and cousins don't, for instance).