The tiny decks builders install are basically there to meet code requirements and not creature comforts. Builders can't leave you with a 3 foot drop off the back door so they often build the cheapest landing and step combination possible, then offer you a real deck or patio at major upgrade costs. While builders are entitled to a profit, this is one improvement that can be done far more inexpensively after you move in.
Deciding whether a deck or patio makes the most sense is part structural and part personal choice. If your back door is close to the ground (within a foot or two), we would definitely recommend going with a patio. Decks require more vertical space for the posts, beams and joists to be built and it makes no sense whatsoever to build those below grade. If a patio is your pick, you can build a super nice one with concrete pavers. These are modular bricks and fit together like puzzle pieces. The most important part of the installation is the preparation of the base. You'll need to clear and flatten the land, then lay down 8-10 inches of crushed gravel and tamp it until it is almost as solid as concrete. If the base isn't prepared correctly, you'll end up with a patio that looks more like rolling hills punctuated by weeds.
If you have more vertical height off the backdoor or if your yard slopes off so much that a patio wouldn't be practical, building a deck is a terrific option. When designing your deck, first decide whether you want one level or more. Remember that while multiple levels can be very attractive, each one reduces the amount of useable space since furniture can't be placed near step-downs. If a deck is for you, there are many material options. Natural wood choices include pressure treated lumber, cedar, redwood or Ipe, a beautiful and resilient hardwood. Composites, made of plastic and lumber combinations, are extremely popular. Fiberon, for example, is available in many colors and includes modular railing options that will give you virtually a maintenance free deck.