I think the first good step is to look over the dynasty rulesets and see what appeals to you.
They're on our Challenges board, in their own sticky threads. I can give a short overview of the four of them, though:
Immortal Dynasty: Have one sim from each generation complete a set of requirements, become an elder, and eat ambrosia, until you have eight immortal elders living under one roof.
Townie Decadynasty: Have one sim from each generation complete a set of requirements and marry someone else who lives in town and move into their house, until you have ten generations that have lived in ten houses.
Life States Dynasty: Have one sim from each generation that's of a unique life state complete a set of requirements, until you have seven sims of different life states under one roof.
4x4 Dynasty: Have one sim from each generation complete a set of requirements, and move town every four generations, until you have sixteen generations that have lived in four towns.
They all get a lot more in depth than I can convey in one sentence.
The biggest part of a dynasty is the rules and requirements that each heir needs to adhere to, which is great for players that like goal-oriented games. It also means that reading the rules and posting on the threads with questions is essential. Don't feel bad about asking questions because some of us just love answering them.
As for which one to do first, it's a matter of opinion, but I find the Immortal and Life States Dynasties to be a little more beginner-friendly.
And also, welcome to the forum and to TS3 in general.