I use Coinbase.
1. Why did you choose that exchanger?
At the time it was the easiest way for my to buy cryptocurrency. It's also a local company for me, which give me trust (albeit a fals sense) that the business was sound.
2. What was the verification like? ( was photo ID, address bill, credit card picture, etc needed)
Thorough. Personal information and photo ID. There's no anonymity and I'm OK with it.
3. How long did it take to get your crypto?
The first time took a week or two because I had to get my identity verified. Now, if I want to buy crypto from Coinbase I can do a direct debit from my bank account, which costs 2.99% and takes 5 days to settle. Or I can use a credit card for my purchases, which costs 5.99% and takes 48 hours to settle. Either way I look in my buy price when I click "Buy".
To the OP, Bitcoin exchanges available to someone are still largely aligned by Country. It's easiest to work with an exchange that's based out of your country or Region of the world.