My first tip is before you buy by mail or online, check your local nursery for the plants you want. There are lots of great nurseries, and buying locally is not only good for communities, you can usually not only get plants, you can get advice and often, given the high cost of shipping, it will be cheaper. Also, if you are buying perennials, trees or shrubs, you are more likely to get plants that will grow well in your area.
If you are buying plants online, make sure to really read the fine print about the size of the plant you will receive. Photographs in catalogs and online can be really deceptive--showing large fabulous plants, when what you are actually getting is a much smaller plant--sometimes just a tiny sprig.
Beware of shipping costs. While you might think you are getting a great deal, sometimes if you factor in shipping, it will cost much more than you might think. It is expensive to ship plants because they need fast shipping and special packing requirements.
Check the quality policy. While most plants I've bought by mail have been fine to spectacular, some have come in terrible shape. Most places I have dealt with have been really great about replacing damaged plants. However, before you buy, make sure there is a quality policy that let's you get replacement plants easily and quickly.
Buy from reputable companies. There are many fantastic online purveyors, that are dedicated to shipping beautiful and healthy plants. Make sure to buy from these companies, otherwise you risk getting diseased or unhealthy plants that can spread insects or illness to your healthy plants.
Here are a few suggestions for places I've had good experiences with: