Not used one myself but if you want to be completely anonymous you could use a Bitcoin ATM, I believe you just need a wallet address. You can find a list here -
https://coinatmradar.com/, other option is to buy them locally and in person from someone. Personally I've used Bittylicious which has worked well, you do need to verify your identify though
We don't normally gets worry when buying bitcoin since my wallet is capable of buying and selling bitcoin and ethereum. Coins.ph is really trusted and recommendable wallet, it has also many payment transaction to do like paying electricity bills and telecomms. Buying bitcoin on some exchanges will costs you more than buying on wallet.