Hi Ryan, there are several options available. If you’re REALLY in a rush and want to get in the current dip (have a look it’s going up again, now might be a good time), you can buy ADA straight with your credit card, but with higher fees (2 or 3% I think) on Coinspot, then move your coins to your Daedalus wallet on your computer, where they’re safer than on the exchange, where you do not own them technically speaking.
Most of us trade on either Bittrex (US), Binance ( HK), UpBit or Coinnest (KOR). Here is the full list of the exchanges listing ADA so far. Registration can take from days to weeks on these exchanges depending on where you’re based, and due to regulations and KYC strict procedures. Generally, wire transfer is preferred as cheaper fees, but it also takes longer to get credited.
See my comment comparing Bittrex and Binance earlier today that might interest you.