I'm interested in starting to play WoW coming from a started account, what happens if I buy and old WoW expansion such as Cataclysm, Wotlk, BC for super cheap and activate it? Will the account upgrade from starter to standard? And will I be able to level-up until bought the expansion level-cap or the 90 which is for the base WoW?
You cannot use an expansion code to activate the base game.
You cannot use an old expansion code for anything since those expansions are included in the base game. Do not buy old expansion codes.
Today, the base game is $20 and comes with a free month (worth $15).
Here is more information about what can be purchased. https://gaming.stackexchange.com/a/144423/9192