So, I have had my wallet at coinbase for a short period of time and have about 0.5BTC as of today. Is it worth moving my wallet to say copay for example and eat up the fee?
I plan on investing further, so should I do the move before sending more to coinbase wallet?
Thanks for any information/help.
If you're serious about investing in BTC, please consider moving your funds away from online wallets...
It's simple really: if you're not the only one in controll of your private keys, you don't controll your funds. In your case, you're depending on the sustainability, goodwill, TOS, support staff, hardware,... at coinbase. If they ever decide to lock your funds, if they become hacked, if they turn scam or if they go bancrupt, you'll be in troubles.
Same goes for any online wallet provider (including blockchain.info). Even if the online wallet provider gives you access to the private keys, you must realise it's possible they also have access to these keys, so in this case, they can still get hacked or use your unspent inputs to create tx's themselfs.
The safest alternatives for long term storage are:
Paper wallets, hardware wallets or offline (cold) storage.
In case this is to expensive or to complex, a decent desktop wallet on a clean PC, with decent backups will do the trick to... You can pick any decent wallet, like bitcoin core or armory (they need to sync the full blockchain tough, so it'll take a while before you can start using them + they'll take up ~+100Gb of diskspace unless you prune your db).
If this sounds unacceptable to you, you could also go for an SPV HD wallet like electrum or multibit HD (these wallets only download the block headers, and they use a seed phrase to generate all private keys/public keys/addresses, so you only need to backup this one phrase to backup everthing).
The main point is that by using desktop wallets, paper wallet, hardware wallets or offline wallets, you're the only one controlling your private key, so you're the only one in controll of your funds.
If, for some reason, the wallet dev's stop working on the wallet, you can just move your funds to a different (supported) wallet. Using the seed, exported private keys, xprv, you should be able to restore your private keys and import them in a different wallet even if you can no longer access the wallet itself (for example: if you would chose to use the electrum wallet, but the development stops and all the electrum servers go offline, you can still use the seed to create the xprv, and generate all private keys for all addresses that were in your wallet... This isn't an easy process, but it can be done)