Based on your choose, which one exchange market do you use and how secure so far when saving assets there, I think Binance and Kucoin still on the top securing exchange for holding our Bitcoin assets, better purchase Bitcoin with with fund $60 than purchasing cold wallet but don't have assets yet.
No, no and no. There is no exchange that is safe and secure for saving your crypto assets, just look above your screen on this website, look to the news update theymos has pinned above, online accounts or centralized exchanges are not safe for anyone to save their funds there, you may not lose it today, but you may someday.
Binance isn't safe, they have been doing shady stuffs for a long time, just that they are yet to run into trouble, it does not mean they wouldn't, Sam Bankman-Fried was doing shady stuffs with people's money for a long time, but it only took a week for everything to completely collapse and for people, and the exchange too to go bankrupt, and hacked too by the way.
Hold your funds in your self custody, trade on decentralized exchanges that is trustless; with binance, even in their p2p service you have to trust binance, in decentralized exchanges like Bisq you do not trust anybody, and you would not lose your data to the exchange.