...At the moment I think that BUSD and USDT are the safest stablecoin pairs for regular cryptocurrency trading but I'm afraid that Binance has so huge influence on the market that if it makes mistake, BUSD may get fucked...
Your concerns are not unfounded, since the security of BUSD directly depends on the security of the Binance exchange. But at the same time, you should remember that BUSD aud USDT are centralized stablecoins, unlike decentralized DAI. Thus, if you are a supporter of decentralization, then it would be logical to use decentralized stablecoins.