A bitcoin wallet differs from a traditional wallet in that the bitcoin wallet contains no money but only the private keys. People's money is stolen not because their wallets are missing but because someone else knows the words string of the private keys in the wallet. Therefore, a wallet could be a paper written the words string of your private key or your brain to memorize the words string of your private key. In fact, the so-called bitcoin wallet app or software or web service in this sense is logically only the ATM to operate with the bitcoin network and shall be named as wallet only happen to be the device to store the private keys. You shall be free to store your private keys wherever you prefer and whatever format you prefer. If a wallet service provider disallows you to move your private keys, it must be a scam or potentially a risk. It is a conceptually trivial task to back up your private keys. If you feel it complicate, the reason is highly possible that in order to provide additional service, the service providers intend to store your private keys remotely in their site and need you to cooperate some additional encryption tasks for safety sake. The number of balance reported by a wallet may be incorrect and miss-leading because a wallet usually sums only the balance contributed by the transaction done through the wallet. The only way to get the correct balance info shall be query through the blockchain directly.
A mistake in bitcoin operation is almost irreversible and there is no toll free phone number to call help; see here and you may wonder so many spikes which are exactly fee-mistake transactions and the spenders cry out loud. Therefore you may try some free fake money to gain some operation experience in the testing bitcoin network testnet rather than the production bitcoin network mainnet first. You can go to here to get some free testing money and try in some testnet wallet.
Different designer of the wallet has different target users. Some are simple but not delicate (for example copay) and some are delicate but not simple (for example Bitcoin Core) or something in between like coinb. By the core API, wallets may have these features:
For me, I don't like to store or send the private keys (even encrypted) remotely and I don't like to use the program I don't have the source code. So I prefer a local copy of rein project as signature tool and coinb as the ATM. However, this is a personal preference about the risk and convenience.
Any transaction needs fee unless it is a barter. In typical gold banking, the fee is to help the bank to cover the cost of transaction document; without a decent recording of documents, the gold can be double spent. Likewise, the fee in bitcoin transaction is to help the 'digital document' saved in the blockchain from double-spending problem. It is impossible to have global public consensus about "who owns how much" without cost.
The fee can be arbitrary. However, for those who maintain the blockchain (the miners), they will include high fee transaction into their blockchain than low fee transaction. If you insist a tiny fee, you may wait indefinite time for its including into the blockchain. A cautious merchant may not be willing to deliver the service/goods unless there are 6 more blocks deep for your transaction in the blockchain. Therefore, the fee rule is: you want fast, higher fee. The factory default fee of a wallet may not fit your preference. From time to time, you'd better see the page to set a proper fee for your transaction where it shows the fee per byte and the estimated time into the block. A typical two inputs two outputs transaction is 274 byte long. If you think the estimated fee is too expansive compared with your transaction, don't use the bitcoin for it, just like you will never use gold in fast food restaurants because they won't bother to spend the time to measure the weight of your tiny gold.
Explain the philosophy behind BTC to your friends if you can. Too many scams because people don't comprehend. Bitcoin is not about gambling or speculating or cheating. Instead, it was invented for economics welfare. Everyone, not only the 1% people, deserves a better life. The more people appreciate the logic, the more goods will be traded in BTC, the more goods will be valued correctly, the more equally the wealth to be distributed, the less wealth stolen by the 1% people and the country.