1:
Well, you can decide for yourself on the exchange websites what you would like to receive. For example, you can decide that OMNI chain (via the Bitcoin network) or ERC20 (via the Ethereum network) or TRC20 (via the Tron network).
But note that USDT in the three networks is not interoperable.
Each type of chain has its own advantages and disadvantages, you can choose according to your own assets.
Main differences between the three chain types
USDT-OMNI is the USDT issued by Tether based on the BTC network.
The currency deposit address is the BTC address; the deposit and withdrawal will be taking place on the BTC network.
The protocol used by USDT-Omni is the Omni layer protocol built on the BTC blockchain network.
USDT-ERC20 is the USDT issued by Tether based on the ETH network.
Its deposit address is the ETH address and its deposit and withdrawal use the ETH network.
The protocol of USDT-ERC20 is the ERC20 protocol.
USDT-TRC20 is the USDT issued by Tether based on the TRON network.
The currency deposit address is the TRON address, and the deposit and withdrawal will be taking place on the TRON network.
The TRC20-USDT uses the TRC20 protocol.
2:
I always recommend to buy Crypto through AgoraDesk / LocalMonero (They are basically the same with different Domains, so it doesn’t matter which one to use), since you not necessarily need to go through any KYC details.
But if you don’t care about your transaction / wallet being tied to your ID you can of course use any exchange like Binance or so.