As a bitcoin nerd, I would advise a few things:
If you live in the USA, the easiest place is to use
Coinbase.
If you're inside the SEPA zone, use
Bitstamp.net.
Both services are very reputable and contribute a lot to the bitcoin community. If you live elsewhere, I'm not sure who the best vendor currently is.
If you verify with Coinbase, they'll speed up your delivery on coins, but everything is done as a market order, so you're locked in at the price at which you buy them. Example: you buy 1 BTC at $650, but you don't receive it for 3-5 days. Within the 3-5 days, the price spikes. You still get 1 BTC for $650.
I'd recommend subscribing to
r/bitcoinmarkets (there's a lot of wisdom if you can look beyond the speculation bullshit), and also there is an IRC channel (#bitcoinmarkets) that serves as a live chat area.
My favorite graphs are
markets.thegenesisblock.com.
I usually look at the order book for MtGox even though I buy at Coinbase. DO NOT BUY OR SELL FROM MTGOX. They are having a lot of banking issues and until they sort them out, it's not a feasible exchange for a small-time investor.