The short answer
For USDT, pick Tron (TRC20) unless your sportsbook does not support it. TRC20 costs about $1 per transfer and takes 1-3 minutes. Almost every offshore sportsbook supports TRC20. This is the default choice.
When to use ERC20 instead
If your sportsbook supports only ERC20 (rare), or if you are moving large amounts (five figures or more) and prefer the liquidity depth of Ethereum. ERC20 costs $2-$20 per transfer and takes 2-15 minutes.
When to use BEP20
Only if your sportsbook specifically requires it. BEP20 is cheap (under $1) and fast (under 2 minutes), but its smaller. Stake, Rainbet, and a handful of others support it. 1xBet does, bet365 does not.
When to use Solana
Increasingly supported, especially at newer crypto books. Very fast (under 30 seconds) and cheap (under $0.01). If it is an option at your sportsbook and on your exchange, it is competitive with Tron.
Bitcoin networks
Bitcoin has only one mainstream network (Bitcoin mainnet) plus the Lightning Network. Most sportsbooks accept Bitcoin mainnet with 1 confirmation, which takes 10-40 minutes. Lightning is instant and cheap but support is still rare at sportsbooks. Stake supports Lightning; most others do not.
Common mistakes to avoid
Sending TRC20 to an ERC20-only address (funds lost). Sending BEP20 USDT when the sportsbook expects TRC20 (funds usually recoverable via support but slow). Not double-checking the network label in your exchange withdrawal. Always verify the network match before confirming the send.