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Arborvitae don't take well to pruning. You can do it but it may result in bare spots or mis-shaping in the plant. Your better course of action is to repot the plant into a bigger pot and this would stop the falling over.

If repotting is not an option, you can prune. Just proceed slowly and realize that if you cut growth off near the top, you will permanently restrict the height of the plant. You should only prune to reshape the plant and any deep pruning (where you cut off entire branches) will not likely grow back.

This will help;
https://www.gardeningknowhow.com/ornamental/trees/arborvitae/winter-damage-to-arborvitae.htm

Fertilize this shrub 3 times a year.
March 30, June 30 and Sept. 30.
Use a slow release fertilizer.
NPK numbers of 12-6-8 or 14-7-7 will benefit your shrub.

Sprinkle around the dripline of plant, do not mix into the soil.

On planting it is recommended to sprinkle one tablespoon of lime around the dripline.

Topping arborvitae is not recommended. These articles explain why, and what you can do instead:
http://www.pennlive.com/gardening/2015/07/topping_a_line_of_too-tall_eve.html
https://ask.extension.org/questions/164462

I worked at greenhouses and for landscapers over the years, and the answer most given to this question is, 'buy the largest tree specimen that you can afford'.

You always need to consider how fast a tree specimen's growth rate is and in the case of a Thuja Green Giant, they are very fast growers.
So choose a healthy plant and do not worry so much on the size you are starting with.

Smaller plants can be less stressed by transplant shock.

Arborvitae shrubs or trees require a deep, thorough watering immediately after planting to settle soil around the roots and remove air pockets. For the first year following transplant, arborvitae typically require weekly soaking in the form of rain or supplemental irrigation. Arborvitae planted in sandy soils or containers may require more frequent watering, especially when conditions are hot and dry. Applying water in the form of a slow trickle that penetrates the ground and soaks the entire root mass is crucial.
https://www.gardeningknowhow.com/ornamental/trees/arborvitae/growing-arborvitae-trees.htm
https://www.gardeningknowhow.com/ornamental/trees/arborvitae/fertilizing-arborvitae-trees.htm