For $50, I'd do some research on the manufacturer and such just to make sure they are legit and have ok reviews. Also, is it new or used? That is a little below what I would expecting to pay for a new lower. But in the grand scheme, IMO, there are very few functional differences in the lowers. Now on a real nice one you might have more attention to detail and better quality control, but the vast majority of less expensive ones seem to come out of a handful of factories across the country and often the only difference is the logo etched on the side.
Keep in mind that the lower is the part considered a firearm and must be registered, so you will have to deal with shipping to an FFL who can transfer it to you. Their fee for this service will add up in the total cost. I can go and find them locally for $90 or so normally at shops, so if I bought the $50 one online, after paying the (overpriced) $30 transfer fee I wouldn't be saving too much.
Your build sounds like it could be done very economically, good luck!