Let's say you are new to cryptocurrency world and your first wallet is on blockchain.info, and you have managed your first hurdle of gaining level 3. (can deposit/withdraw max 8000 GBP) Your wallet contains 16,000 GBP and you managed to buy at a rate giving you four bitcoins (for 4000 GBP each for example) the market explodes and bitcoins are now worth 20,000GBP each. You now decide to take 50% profit but you are only allowed to sell 8000 per 24 hours by which time the market has crashed again - by what method would best allow instant liquidity in this position - in crypto for dummies style please.
First, it is not recommended to store huge amount on online wallet.
I highly recommend GDAX.com(they are part of Coinbase) for that purpose, even if you are affected by a withdrawal limit there, you can still trade fiat/coins <-> coins/fiat freely. Also they have super low fees on trades.
What traders usually do is to deposit fiat to Coinbase, then move fiat free of charge to GDAX, and execute tradings there at no fee/low fee. For storing, you better use a cold wallet.
I will agree with Chak. Storing all your currency in online wallet is very risky. It's very dangerous 'cause you may lose all tour capital this way. I think it’s better to leave small amount of money into online wallet and transfer the rest to hardware one. This way your funds will be safer. Alternatively, you can obtain a wallet with cold storage. For instance, cex provides such wallets. By the way, they offer bonuses for using wire transfer payments, https://cex.io/wires-campaign/.