I highly suggest that you do not use any web wallet (e.g. blockchain.info). You should use a wallet that is created locally and properly back it up. All of the most popular wallet software have instructions on backing up and will usually instruct you to do so before using the wallet.
I suggest that you use Mycelium or Electrum. In general any wallet listed on
https://bitcoin.org/en/choose-your-wallet is a good choice.
Regarding buying Bitcoin with western union, few exchanges allow that. If you want to do such transfers to buy Bitcoin, I suggest that you find a trader on localbitcoins.com and get your Bitcoin there. Just be sure to check the feedback ratings of the person you are trading with and always use the LocalBitcoins escrow.