「はじめまして」 would be preferable to 「はじめました」
「はじめまして」as a greeting is not the conjugated form of the verb はじめる
「はじめまして」as a greeting derives from 「初めてお目にかかります」 "I meet you for the first time" or more literally, "You see me for the first time".
I am sure you already know it is a common greeting, equivalent of "How do you do".
As for the difference between はじめる and はじまる、the former is a transitive verb while the latter is an intransitive verb.
If you really want to learn Japanese, take lessons. Trust me on that one. And make sure there are plenty of opportunities to speak the language as well as write it.
Spoken, Japanese is a fairly easy language. Written it's one of the hardest.
Oh and welcome to AO.