A Red pullet is most likely a Rhode Island Red or Red Sex-link pullet. Pullet is not a breed, but rather the name of a very young hen. It is possible to guess the breed of a particular chick if you have a photo guide of what the different breeds look like when first hatched. This is, however, not a guarantee, since a large majority of breeds are born buff yellow, and change as they mature into their true feathers. Aside from sex-linked breeds, it is almost impossible to identify male vs female with 100% accuracy with new born chicks. Chicks labeled pullets that do not have any true feathers yet are only about 75-80% likely to be female.
As for buying from TSC, I have not had any problem with getting healthy chicks from them or any other 'feed store' that offers baby chicks. Because they will usually get a 'straight-run mix' or 'pullets mix', you can not be terribly selective in what breed you get, and anything from a 'straight-run mix' is 50/50 on whether you are buying males or females, because 'straight-run' means they have not been sorted by sex.
If you want a specific breed, ask TSC, or another feed store, if they do special orders. Some places do, and they will add your order to their next chick order and reserve your chicks for you. Another alternative to getting a specific breed is to go through a direct order company, such as Cackle Hatchery or Murray McMurray, to name just two. This option has it's own draw back, since you must order a minimum number of chicks (15-20) to ensure they do not get chilled in transit, they are delivered to your local post office not your house, and you must pick them up there.
A final option is to ask around among your neighbors, and see if they, or someone they know, has chickens, has a rooster (so you have fertilized eggs being laid), and offer to buy or trade for some (to either hatch your self or to pick up once they have hatched).
Hope this helps.