Definitely strapless bra and nude coloured undies.
Try something in every style if you can to get an idea of what suits your body shape.
Take a pair of heels if you're planning to do heels on the day as you'll stand differently in heels which will make a difference to the look and fit of the dress.
If this is a scouting mission (e.g. You're not sure if you're ready to buy yet and just trying to figure out what suits) take a pad and pen and write the names of designers and dresses you like. You won't be allowed to take photos until you've ordered the dress.
Forget 'normal' fashion sizing. Bridal sizes are a bit out sometimes, and most advice is to order a size up so you can alter down.
Be prepared to stump up a 50% deposit.
Most importantly:
Set your budget. How much are you really willing to spend and does that include embellishments like veil, headdress, alterations etc. Alterations can be quite pricey so make sure that the whole package is affordable.
Don't try on ANY dress that is over budget. The odds are that you fall in love with it and will either go way over budget to have it or have to walk away and regret it (this happened to me).
Tell the assistants what your budget is and they will find you an array of dresses to try on that you know you can afford.
My mistake was goin into a boutique and trying on all sorts of gowns that I chose off the rails, because that's what they do on films, right? Terrible idea. I fell in love with a gown I couldn't afford and regret it to this day 10 yrs on. I loved the dress I eventually got but it still wasn't a patch on the first one.