If you are careless with anything, there is a high probability that you are going to lose that thing, not only bitcoin. There is no universally accepted method of exchange that can be called the cheapest and safest, it would depend on the individual and what they are looking for. The Bitcoin network is safe, but the safety of the bitcoin in your wallet depends solely on you and your actions and inactions, as for cost, bitcoin is cheap for cross-border payments and with the current state of the mempool, it is cheap for local transactions as well.