The bottom half. If you carry your fat at the top of your hips, as I do, rather than around your thighs, you are likely to suit a dress which hangs straight. (Image 1. Me in a straight skirt) If you carry more weight around your thighs (rather than the top of your hips) you will suit an A-line or flared shape skirt. Wolf & Badger (London), a company which sells clothes from independent retailers, have a great selection of wrap, waisted and flared Summer dresses to choose from. Here is one showing how the flared shape will follow the natural line of your body.
One of the most stylish ladies I have known is an apple shape (she is petite and her waist is as big or bigger than her bust). Her secret has been to wear dresses gathered from the top, with and open V or scoop neck and bring interest near her face with necklaces, earrings and scarves. Here is another beauty from Wolf & Badger which will suit you.
You need a slender neck to wear a dress with a high neck. The longer the better - the neck, not the dress! (Think Laura Kuehnsberg). The coral coloured Whistles dress (Image 3 below) can be buttoned up for swans and opened up a button or two if your neck is short.
Can you wear a midi or long dress? If you are a long, tall Sally, no problem. You can even team this beautiful Pazuki dress (also available from Sheen Uncovered and Ruby Blue) with trainers. A word of warning though! I am 5'5" and I definitely need heels to rock a midi. In flat shoes I just look dowdy. Petites will look better in shorter dresses. The sweet spot for dress lengths is where your leg goes in to its own bone - often just below the knee.
What is your view of sleeves? Although reasonably fit, I do not want to wear sleeveless dresses on account of elephant's backside armpits. 3/4 length sleeves rather than full length give the effect of longer legs but when it gets really hot you may not even want that. More and more dresses now seem to offer that bit of coverage while allowing air circulation! Here are two: A silk wrap Primrose Park dress (below) from Sheen Uncovered and Ruby Blue and chic linen straight number from Jigsaw