self, irish/english-irish, berkshire, hooded, without any headspots or facial markings is very important to raising quality offspring
She has already gone over some good markings:

Self (or solid color),
Berkshires (belly is white)
Irish (small heart of white on chest)
Hooded or bareback (color on head, neck and shoulders with a stripe running down the back, barebacks have no stripe down the back)
Notched cap (color on head with small indent on the back)

Coats:
Straight
Wavy
Rex
Harly

Safe Colors:
Black
Brown
Cream/beige
albino/white
fawn
gold
russian blue/grey
agouti/cinnamon

Ears:
Dumbo or normal top


What patterns to avoid :

Baldies/essex (white spots on head,often looks like a bald spot)
Blazes or badger (white from nose and spread up to the ears)
Odd-eyed rats, often with blazes (one red eye, one black eye, sometimes the red eye looks black unless light shined into)
Lightning marks on face or split caps (split cap looks like a capped rat, but their is a line going through the middle of the head)
Black eyed white rats
Banded/husky/roan rats (looks like a high sided berkshire, a long band of color down back of animal)

High white rats (rats with irregular patches of color, can be combined with any before stated markings, )

Colors to avoid:
English blues from pets store: often weak immune systems, prone to many problems and die young. (buy from established breeder)

Merle and pearl: Pearl is homozygous lethal and can accompany merle.

Coats:
Hairless or fuzzy
tailless


I think that's really it. If I forgot something or made a mistake, please feel free to correct.