You'll get every type of response on this topic from "real bassist don't use picks" to "I use a .38mm (REALLY thin) cause I can play faster". My advice is to determine two things; 1- the thickness you like and 2- the shape you like. It's all subjective really. There are many thicknesses to pick from but most bass pick players tend to use anything from .88 mm on up to 3 mm with most falling around 1mm. There are three basic shapes that are most popular, the triangle (also called a 348), the "standard shape" (pointed triangle or 351) and a smaller teardrop shape (called a jazz or 358). There are other shapes but these are the most prevalent. What you need to do is go down to your local music store, or order online, and buy a few picks in various shapes and thicknesses. By trial and error, you will be able to decide what is best for YOU! Don't play a brand/thickness just because your favorite bassist use one, use what's right for you. Now, what I use is a standard Clayton Acetal 1mm. I like it cause it the style I used when playing guitar and the Clayton's seem to be a bit bigger than everyone elses standards. I have used Dunlop nylons in 1mm and the Tortexs in 1 and 1.14 mm and they are good picks. But trying to find the perfect pick is kinda hopeless, like finding the perfect strings, but just have fun and enjoy the hunt!
Another useful consideration is overall size of the pick. I used to pick with Fender "Heavy" (can't recall the thickness). This one was ok, but the pick is small and it was hard to relax my grip - otherwise the pick would slip at the worst possible moment. This was especially true playing gigs outside in hot/humid weather.
Last year I visited Gelb Music in Redwood City, CA. They have an excellent selection of picks. Ed, their resident bass expert, recommended a pick made by "Cool" that is "Heavy / 1.0mm." It's about 1/3 larger in size and has a rubber insert. This combination of features makes it very easy to grip, easy to pick, and nearly impossible to slip. I haven't looked back. So +1 to the "try 'em and see what you like" philosophy.

