For storing Bitcoin, I would definitely not recommend CEXs (unless you are a day trader). For mobile wallets, Trust Wallet is the one that I trust the most because it’s decentralized, non-custodial and we own the private keys to our coins or tokens.

I have used Bitcoin.com wallet before during a blockchain conference in Manila. I met Roger Ver in person there, took a picture with him, and he sent me $10 worth of BCH that time to my Bitcoin.com wallet. But eventually, I withdrew it afterward lol.

You are not getting it completely right. If it is electrum on computer, definitely you are right, you can edit the fee by also typing it, you can even edit the fee to be 1 Satoshi/byte. This is why electrum desktop wallet can be used to even consolidate. But on mobile electrum, you can although still edit the fee but you can not edit it by typing, it only gives five editing means which you can see in the below diagrams, and it can not edit for transactions that can be below 25 blocks estimate fee. On the mobile electrum, fees can not be edited by typing it.

                    

Only One Word TRUST WALLET Simple Interface and easy to use most secure app for you android/Apple

People use different types of mobile wallets for their purposes. Some of the most used wallets are called trust wallet, Tronwallet, wombat, Tezbox, and also many wallets. Of all these wallets, however, my favorite is the Trust Wallet because it seems to be convenient and reliable to use.

With mobile wallets, I use electrum and moved from that to my celium because I prefer it and the interface and how it works better. Desktop I use exodus and long term hodl ledger wallet.
Ledger counts as a sort of bank account while the desktop wallet exodus is for trading and larger purchases sometimes. The mobile wallets I don't keep much on just a spendable amount for smaller things.

For a customizable fee, you can use a decentralized wallet or if you want to really go with Bitcoin, I advise you to buy a hardware wallet since most of the hardware wallet brands have support for mobile devices. It will not just make the transactions easier but it will boost the security of your funds compared to a usual cryptocurrency mobile app wallet wherein the private key of your account is visible. Once it was taken from you through a screenshot or screen recording, your account is already compromised. A hardware wallet is also flexible, you can use it to connect it to other software without the risk as it will never display your private key. In addition, if you want to prove the ownership of your wallet, you can easily use it to sign a message.

Now there are many choices of mobile wallets for cryptocurrency, and the problem is not all mobile wallets are safe and comfortable to use.
I recommend Trust wallets to be used to store Bitcoin that we have. There are lots of benefits provided by the Trust wallet for its users.
Some of the benefits that I feel when using a Trust wallet are fast transactions, can see graphs of price movements, and is safe from hackers.

Many good wallet available.i use trust wallet and blackchain wallet

I am using to save my Bitcoin Atomic Wallet and the experience has been good. I have downloaded other mobile Wallets such as BlueWallet and TrustWallet but I have not used them yet, it all depends on the needs of each person.

I like the Atomic Wallet because in addition to being able to save my Bitcoin I can swap several coins, stake some coins and earn Cashback for each exchange.

For Ethereum I keep my ether and tokens in MEW and MetaMask. Now MetaMask has a useful and convenient alliance with Uniswap from the desktop version which allows me to save time and money.

I suggest you, try to use any hardware wallet cause the current BTC price is really too high. Everyone should get in the habit of using hardware wallet for their own safety.
If you want to store a low volume of BTC for a short time holding then you can use software wallet. You can go with BlueWallet for your mobile, BlueWallet is much Economical, cause its supports Lightning network, by using LN service you can reduce your transaction fees.