...i heard you should check out a variety and shop for the best deal. Makes sense to me, but doesn't that reflect on your credit report that they're all looking?

Yes and no. If they are all within a certain period of time and they are mortgage inquiries, they generally WILL NOT negatively affect it. However, if you want the option of different lenders, go to a broker. S/He will be able to "shop" rates FOR you.