What kind of personality are you looking for? Any breed can have any personality. You can get a good gauge of what they are like in the shelter if you are looking at adults. The personalities of babies often change when they hit puberty, which is partly why so many rabbits are dumped not long after.
In general, the dwarf rabbit breeds are more hyper, which can also lead to them appearing less affectionate if you don't know what to look for. They can also be hard to handle due to their temperament and small size. Plus their little round heads make them prone to tooth problems, so you might want to educate yourself about that (you should anyway, in my opinion). Having said that, I have three dwarfs and I adore them, but I do know some people feel frustrated.
Larger breeds such as New Zealands and French Lops tend to be more relaxed, and giants like the Flemish can be downright lazy sometimes. They do tend to be easier to handle once they are socialized. I do have to say that there's nothing like a big double-armful of bunny, and I would love to have a big bunny of my own sometime. Their cube cages (if you cage them) would need additional support to hold up to their weight and strength.
Medium sized breeds are very common in shelters and include the very popular Dutch and Mini Lop. They are a good compromise- small enough to be easy to house, large enough to pet without feeling like there should be "more" to the bunny (I sometimes feel like this about my dwarfs), and usually somewhere in the middle activity range. I know that my 5 lb Dutch, Loki, feels "right" to me, while my dwarf girls seem to have bigger personalities than bodies.
Really, the best thing you can do is walk into the shelter with an open mind. Don't feel like you have to adopt the cutest bunny if you're not sure that you like his personality (one of mine was rather ugly when I first saw her but developed to have a fantastic, loving personality), and also don't feel like you have to choose one right away for the same reason. And while you're researching, look up info on bonded bunnies. Some rescues may have pairs or even trios available, or will help you bond two of their rabbits.