Is there any kind of inexpensive, prebuilt grow light for growing greens indoors? What if the greens receive some sunlight from a window, too?

Is this any better?

http://vi.raptor.ebaydesc.com/ws/eBayISAPI.dll?ViewItemDescV4&item=112224418614&category=178989&pm=1&ds=0&t=1480751051000&ver=0

There are many of these products on the market, you have found both the extreme low end and the cheaper-end of the low-end. For example, that one from eBay has not been safety tested.

For a 20x10 area you probably "need" something like 5075watts (actual, LED emitted power, some "55w" panels are really 35w), which will run you around $100 or so.

If you have a south facing window, it should give you enough light to grow leafy vegetables. I grew a dwarf tomato without any additional lights during winter. You would get even more light in the summer. It would still get hot, but should slow the bolting down enough to harvest.

If planting spinach, most peat moss based potting mix will have a pH too low for good growth. You would have to add some lime. With your water will also increase the pH. Lettuce and other greens will produce with lower pH.

I did grow lettuce a few years ago under florescent lights, but it was during winter and they do give off alot of heat.

I grow microgreens in Promix in trays, under full spectrum shoplight fixtures. Very easy. It works because the greens are edible in a short time and don't require an elaborate setup.

The light in your links is focused on a tiny area which is good for a tiny pot of greens. You need wider coverage.

Hey, I grow lettuce under this light:

https://www.ebay.com/itm/Mars-300W-LED-Grow-Light-Full-Spectrum-Lamp-Hydroponics-Indoor-Plants-Veg-Flower-/151374521551?hash=item233e9fe4cf

It's full spectrum for all stages indoor plants, I will grow tomato after lettuce

I’ve been using these and am pleased with them

https://www.amazon.com/gp/aw/d/B06XGBKDKZ/ref=ya_aw_od_pi?ie=UTF8&psc=1