What kind of private information would a bitcoin "middleman" ask from clients?
When dealing with established companies as a middelman (usually an exchange), it is common to go through a form of know your customer (KYC). This usually involved some form of national ID, and a bank statement or other proof of residence/address, and is usually done to comply with local laws regarding movement and sale of currencies.

You should, however, be extremely wary of dealing with random companies or people. Make sure you are dealing with a reputable exchange (check review on reddir, yours.org, steem, and other such platforms), and as far as possible, keep any BTC or other crypto in a wallet where you control the private keys (such as electrum, Ledger, Trezor etc). If someone offers to do mining on your behalf, it is almost certainly a scam. If someone says you need to pay to unlock the BTC, it is a scam.

Verify you are dealing with a legitimate entity.