I agree with the discover scuba recommendation above.
In terms of what you need and how much it will cost, search this site or google it with scubaboard as one of the search terms.
The most important thing is to get not only the cost of the course, but all of the extra hidden costs and get a "total-all-in" number when comparing shops and prices.
Most shops make you buy your own mask, fins, snorkel, and booties. This is pretty standard as they are personal fit items. The trick that you have to watch out for is shops that pile on additional equipment requirements that you have to purchase like lead weight, wetsuit, writing slate, and/or knife---some shops might make you buy on of these items some might require all of them. It is a scheme to forcibly generate retail sales and move merchandise and a practice I really don't approve of.
Instruction prices will range from $300-$500 and depend on what is "included".
There are three parts to scuba certification--classroom, pool sessions, open water checkout dives. Some places will include everything in their price (usually in the $500-$600 range) others will break it down with classroom/pool one price, open water dives another--make sure you verify exactly what is included with said price.
Fro the standard recreation scuba class that is not run by an ultra-premium name instructor or agency (GUE, UTD, etc) I would expect the following cost breakdown.
Scuba certification: $500
This will include all pool, classroom, Open Water checkout dives, and any fees to get a physical certification card. All equipment besides mask, fins, snorkel, and booties will be included
Required Equipment: ~$250.
Mask, Fins, snorkel, boots.
The total price for the required equipment can vary wildly based on LDS, brand, and whether the shop gives any student discount.
Mask: Get one that fits, period. A $40 mask is very similar to $100 mask, just make sure it has a good seal on YOUR face.
Fins: A lot of LDS will sell new divers crappy fins for $50-$100 bucks because it is the brand they sell. The fins are some of the most important equipment you can buy and an item I would go elsewhere for if the LDS doesn't have what I need. Mares Avanti Quatros, DiveRite EXTs, OMS Slipstreams, Hollis F1s, Scubapro Jet Fins. The first three are lighter and more suited to a wetsuit diver, the F1s and Jetfins are a little heavier. I am not going to say that those 5 fins are the only fins you should ever buy, but they are certainly the most popular and well regarded fins among experienced divers. You can get all of them for between $90-$120 brand new. If a shop won't sell them to you for that price, leave and go online or to another shop that will.
Boots: Doesn't really matter the brand. I like them with a larger zipper, but it is a personal preference.
Additonal Costs:
1. Possible entry fees to OW dive site
2. Air fills
3. Travel to and from dive sites. possible hotel accommodations, etc
Given slight variations in price and equipment needed I would bracket between $800-$1000 dollars to get certified. This is money that will cover all the extraneous expenses in addition to total certification.
And then there are all of the other classes you need to take to actually become a good diver.......but that is another post