I am sure there must some place to store my inventory rather than carrying all the time with me in my bags. I just dont know where it is. Right now I am back to Arathi highlands to finish some pending quests (lol I am now 33)
Yes, there is! In any major town, you just need to visit the Bank. It should fit your needs.
According to WoWWiki, there are banks in the following cities:
And for some neutral cities:
Also according to the wiki, there are portable banks as well, but I have never had any personal experience with them. You should also find the guild banks there, which are (depending on your guild setup) accessible by the whole guild.
There is also a secondary storage facility available in Stormwind and Orgrimmar called Void Storage. It requires a gold amount (100g currently) to unlock. It has certain limitations:
The upside of all these caveats is:
Think of it as an extended bank for gear you might want to hold onto one day for looks, but won't use ever in the immediate future.
What you are looking for is the bank that supplies some initial space and the option to buy bag slots for additional space.
I know of 3 ways to access your bank remotely: