The big worry with condensation is diseases. Especially with small plants, too much humidity is fatal. So you must figure out a way to ventilate. I don't know how much money you can afford to spend, but floating row covers would do what you need them to do. Check out, for instance, Peaceful Valley's website.
If you want to experiment with the plastic boxes, you could -
drill ventilation holes in them
prop them up a few inches from the soil during the day
use boxes that are at least twice as tall as your seedlings, use them right side up (cut the bottoms to accommodate your plants) and take the lids off during the day (if it's not raining) and replace the cover at night
Those teepee-shaped tomato cages that you buy at big box stores? They are worthless for supporting full-grown tomatoes, but they can make great plant protectors for not huge amounts of money. Use some bent wire to
staple them to the ground, wide end down, narrow end up. Wrap them in clear plastic - heavy weight painter's plastic works - and fasten with duct tape or clothespins (you'll have to pleat the plastic to get a reasonable fit). Leave the top open. Your plants will be protected from wind, you will get a noticeable amount of heat gain, and the open top will prevent excessive humidity. By the time the plant starts to outgrow it's teepee, it
should be warm
enough to remove the teepee completely. For plants that will need support, you can then surround them with a proper cage. I make my cages from woven fencing, from four panels at least four feet tall by 18" wide, fastening the panels together with hog rings. They easily fold flat for next year.
