I joined coinbase, do I trade, or do I just leave the BTC in my coinbase wallet, if the market price go's up, nothing for me to do, just hold the coin in my wallet and BTC go's up in price, my BTC in my wallet increases as well?
You should not hold your coins in your coinbase (or any other exchange for that matter) account for extended periods of time. If you are only looking for a long term investment, you should transfer all your coins off of the exchange.
If you are looking to participate in higher frequency trading that involves day-to-day trading activity you should set a side a certain amount of money (or BTC) to do that with and leave only that much on your coinbase account at a time. The main "base" of your holdings should be taken off the exchange as soon as it is available and stored by you in paper storage or some sort of secure wallet that you have complete control over. If you store your BTC in keys that you alone control, you can rest assured that it is as secure as the entire bitcoin network itself. If you leave them on coinbase you are trusing coinbase with your money, and although coinbase is a "reputable" entity in this space, their future actions are totally unpredictable and you may not be protected by a justice system in the event of your funds being compromised