There are so many different bras out there is easy to become overwhelmed and disheartened.
Some of the most common styles are
T-Shirt Bras- Smooth cup, can be contoured or soft cup but are designed to be worn under firmer fitting clothing. Often a fuller cup also. A good everyday basic.
Balconette Bras- More of half cup style bra. Shows off more of the bust and is well suited to those who are not necessarily fleshy enough up top to wear a full cup bra. Is probably the most flattering bra on the widest range of body shapes.
Push-Up Bras- Often looks like a T-shirt bra but has inner cushioning inside the cup. Can be in the form of air pockets, cushion padding, water or gel pockets. People wear these to get extra lift from their bra. They often only go to a D cup. Probably not the best style of bra for everyday wear however good with lower cut clothing when worn in the right size.
Contour Bras- any bra which has an outer shell on it. Most people call them 'padded' bras. They have a countour to define shape and work well for hiding nipple show.
Soft Cup or Underwire Bras- A bra with an underwire in it but no countour or 'padding' in the cup. Often can be more supportive and fuller in terms of coverage than a contour bra, dependent on the cut and seams within the cup. General rule of thumb is the more seams in the cup of a soft cup bra, the more supportive that bra will be.
Non-Underwire Bra- Can be contoured or soft cup and are worn for a variety of reasons. Most commonly post-surgery bras or training bras for young girls. Quite comfortable but usually not as supportive as an underwire bra.
There are also bras known as 'Specialty Bras'. These are things like Maternity Bras, Strapless and convertible Bras, Sports Bras, U-Bras, and Bridal lingerie. Sometimes these bras need to be fitted slightly differently to normal bras but that might all get a bit complicated to get into!