What is the most convenient network to exchange them and through which site?
TRON is a little bit disturbing, but still admittedly, I have to say that its logical because I'm not 100% confident how other networks fund the processing costs.
You basically need to purchase a TON of TRON and stack it here
https://tronscan.org/#/wallet/resources
It will get blocked for 14 days. For that period, you will be receiving a very worthy amount of ENERGY. You also will need Bandwidth for regular transactions (way less than Energy)
With that energy allocated to your TRON wallet, you will be able to do transactions for free with any TRON hot or cold wallet, from TronLink to Ledger.
So for example I would put $250 in Energy and $250 in Bandwidth and after 14 days you will have plenty of Energy and Bandwidth for your first transactions
Also the higher the payments in USDT through TRON network, the less energy you will need for transactions.
If you prefer to use a exchange like Binance, you will have the good thing here, that they will receive for your the USDT from a TRON network, and then you could change that USDT to whatever you prefer, and move it to pay in a different crypto or a different network.
For example:
1. Your receive 1000 USDT through TRON from that affiliate network to your binance account
2. You change that 1000 USDT to MATIC and move it to your Ledger Polygon network wallet
3. You change that MATIC to almost 995 USDT into your Polygon network wallet (you leave for example $5 in MATIC for future Polygon transaction fees). Now you can pay in USDT through Polygon network without almost any fees
But if you want to keep everything in your own TRON wallet, if you have some money just stake Energy and Bandwidth and everything will be free.