Yeah, crickets from Petco should be fine. As far as I know any feeder from a petstore or "bait" shop online should be parasite-free. My first petshop experience was bad, because I made an uninformed purchase. If you are picking the gecko out, make sure that the tail isn't skinny and that the animal seems lively. If it is a baby, fiestiness is a plus. I have two beauties and they actually came from Petco. They were chunky and tried to bite the clerk when he was "catching" them for me, so I knew that they were doing okay. They are eating healthy and putting on tons of weight, so you can't always assume that Petco animals (or any petshop for that matter) are going to be parasite-ridden or sickly. Similarly, you can't always assume that "online" geckos are going to be parasite-free, so if you get another gecko, keep it quarrantined for a month or two.
A lot of people will advise you not to worry if the gecko doesn't eat right away. I was expecting this from mine, but they all started chowing down within hours of being introduced to their new home, so it really depends on the gecko. Just watch her carefully and make sure that her tail doesn't start shrinking.
It would be a good idea to call a bunch of local vets to find one that has experience with reptiles. It is good to have a vet in advance in case of an emergency. Depending on where you live, it may be difficult to find one and you don't want to scramble at the last second to find one. I'm fortunate enough to live near Washington State University's Veterinary Hospital. If there is a local University that has a Vet Program, they may be a good resource.
My last bit of advice is to just post questions on this forum - there always seems to be somebody knowledgeable who is willing to offer advice!! 
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-Kristin
0.1.2 Leopard Geckos
(Monet, Kumquat, and Tamale)