Not sure this is the most appropriate venue, someone will surely point us to a better place to park this thread!
In the meantime, there are indeed loads of people who can help you, most of whom know far more than me having actually made it to Level-cap (or even Moria!) and played for years more—I only started about a year ago and I've received huge amounts of help
I would recommend that you visit the LOTRO Wiki sometime when you have a free hour or two: you are bound to find more answers there than you have questions
As to your first burning question, there is a place north of Bree name of Hengstacer Farm: the West Bree Stablemaster will charge you for a trip or you can take the free "Bree Festival Ground" horse standing right next to him and head north from where you arrive
The most simple method (there are more complicated methods depending upon what kind of account you have) is to purchase the "Riding Trait" from the LOTRO Store (once per character, there are alternatives which costs more but cover all your characters now and for evermore) and "Steed Skills" from the chap at the farm: these allow you to summon a steed out of thin air. Some people collect them…myself included
Teleporting comes in several flavours. Stablemasters can have the option of "Swift Travel" (which might be available to you again depending upon your account type). Different classes have transport abilities which enable them to jump about the place, sometimes taking their companions with them, sometimes not. Everybody gets a basic Milestone skill, and most people can purchase travel skills to various destinations having jumped through the appropriate hoops.
As you can tell, by how what started out to be a simple reply rapidly got more complicated, this is not a simple subject. If you can locate a podcast called "The LOTRO Academy" they have episodes on most of the questions that are likely to occur to you, from the basic to the really rather advanced: I would advise looking them up and at least trying to read through the list of episodes