I agree that resistance bands would be a good option for strength training workouts. They're pretty inexpensive. You can find them at any Walmart, Target, Sears or even TJ Maxx for cheap.
There are body weight poses in yoga and pilates that do require quite a bit of strength. Will you increase your strength doing yoga or pilates ? how many times a week do you plan on doing them ? While there are many benefits to doing yoga or pilates, once a week may not be enough. It depends on what your fitness goals are.
If your goal is to do a hand stand, you may need to do some extra strength training to increase your upper body strength and balance. If your goal is to just be a bit fitter, 1-3 ST workouts a week would be sufficient.
If you're interested in learning how to use resistance bands as part of your ST workouts, join SERGEANTMAJORs resistance band team. He's got a bunch of beginner to advanced level workouts posted. www.sparkpeople.com/myspark/groups_individ