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So you just need a wallet.

If you have a wallet, you can store your coins there.

There are HOT wallets and COLD wallets. Wallets are where you keep your coins. Once in your wallet/wallets, you can send money from that wallet-address to anyone.

The cold wallets are more secure, as it is a PHYSICAL flash drive that holds your coins(it will have to be mailed to you), and can be disconnected from your PC.

The hot wallets, are online. The way it would typically work, is that when you need to transfer coins TO the exchange, you would take some coins from your COLD Wallet, transfer to your HOT Wallet, which you would then transfer to the exchange. Exchanges and HOT wallets can of course be hacked which has happened in the past. So typically, youd have the bulk of your money in your COLD Wallet offline, until you wanted to deploy it that is.

Obviously you can decide how you want to manage your coins, and where you want to keep them at any given time.

A simple idea, is that you trade small to start, and keep your coins in a free Hot Wallet. And get a COLD wallet by the time you've gotten good with trading, and ready to make larger bets.

The above paragraph is my plan as I'm in the process of setting up accounts and buying coins, and learning to trade. So any small money I start trading with I'm not too worried about. I'm trying to decide between trading with Bitfinex or Bittrex?

Your question about buying from CoinBase... You can buy from coinbase, you just would then transfer those coins you purchase INTO your Hot Wallet. Once in your HOT wallet, you can transfer to the exchange of your choice and trade.

The below is the advice I got from a Good Friend of mine, so I'll share it here.
Good Cold Wallet: https://www.ledgerwallet.com/products/1-ledger-nano
Hot Wallet: https://jaxx.io/

You can buy coins on coinbase then you need to transfer to an exchange like kraken or bittrix, from there you link the API of the exchange to Coinigy.

I am using coinigy + bittrex and work perfect!

If your in the US then as far as I know coinbase is the best place to purchase your coins. It's not the best place for trading as it has limited coins that you could trade. Id recommend accounts with the exchanges Bittrex, Poloniex, Kraken and maybe HitBTC (for small trade coins). Or just pick one to keep it simple. Then send your coins from coinbase over to your exchange account. Then set up the API connections on coinigy with your exchanges.

right now I'm using coinbase to transfer fiat money to crypto and then transferring it out of coinbase to an exchange with more coins available for trading. The issue with coinbase is their fees are pretty high so I only buy in bulk when theres a huge drop . Doing that until I get tier 3 on kraken and can start depositing money straight from my bank without all the fees.