Succ laws:
The ideal succession law is almost always Primogeniture (if you play the "correct" way) or Ultimogeniture (if you game it and divorce/kill your wife after you have an heir you like.) If you're playing without Conclave, then you can get Ultimogeniture pretty easily as long as the local crown authority is at least "Low", and if you're independent and there's no de jure king (e.g. Ireland,) you can get any law you like. If you have Conclave, you need Legalism 3 and "Late Feudal Administration" for either -geniture law, in which case your best bet is Seniority.
Seniority is the ideal succession law for "marriage game" playthroughs where you try to get family members onto foreign thrones rather than conquering them yourself. Without Conclave, it requires Medium crown authority; with Conclave, it's available from the start.
Gavelkind is the most frustrating law, because it divides your titles between your kids when you die. Elective gavelkind is even worse because it creates titles out of thin air if you could hypothetically form them.
Elective is bad unless all your vassals are family members.
Tanistry is available to Celtic characters (Irish, Scottish, Welsh, or Breton.) It's like elective, but you never lose titles because the nominees are your family members, not your vassals. It's great if you have one top-tier title, but trash if you have multiple (e.g. King of England and Wales) because different people will get elected for both titles, especially if you have a large family.
tl;dr Primo, Ultimo, or Seniority
Assassin's Family:
Get a good spymaster who loves you. Check "auto-stop plots" on the intrigue screen. Bribe people who refuse.
Army:
Upgrade the castles you own. Get more land and vassals. Paradox games are not built for playing tall.
Ninja'd by Teneb; alliances are amazing (and my primary strategy when expanding early on,) but make sure you can actually call them into your wars. There's weird rules about that; you can't call foreign powers into wars against other vassals, for example.