Can I buy bitcoins from the exchange market with a local wallet like the Bitcoin client and localbitcoins.com? Or do I have to have something like Mtgox? I looked at the markets for bitcoins and MtGox usually has the largest exchange rate in USD compared to other online wallets. Does the value of Bitcoin increase/decrease based on which online wallet you use?
I am new to Bitcoins and was wondering which exchange website I should use- MtGox, Virvox, BTC- E, etc. What is the difference and do I need one of websites to buy/sell Bitcoins? I have already downloaded the Bitcoin client so, should I just use that to buy of the Market?