You should use search option for your question, there is many threads like yours. Also this is not proper board, move this (check move button) to
Development & Technical DiscussionYour first choice should be
Electrum, it is just what you ask for, it is light ( only need some 40 MB of download after install) , it is easy to use, you are in full control of your private keys and you have backup in form of seed words. Just use link in this post (to avoid fake wallets), create standard wallet and write down seed words ( be very careful with that ). Also set up strong and unique password for wallet.
Armory is not for you since it is also need BitcoinCore to be installed and completely synchronized.
I recommend Blockchain (web: blockchain.info)
Because Blockchain is a trusted and undoubtedly bitcoin wallet. We can see all bitcoin transactions like sending and receiving bitcoins from all blockchain accounts. Its security system can guarantee in every transaction and storage.
Another advantage is that blockchain makes it easy for merchants online merchant by preparing API technology. But behind all the advantages, still have shortcomings such as:
It is only possible to store bitcoin, meaning it can not yet store other coin coins such as etherum, litecoin etc.
For us as Indonesian people, in blockchain there is no bitcoin exchange service with rupiah currency. Instead of using blockchain we have to use another wallet as well.