I view a "beater bike" as a second bike. One has a good bike and a beater bike like one has church clothes and play clothes. What's nice about a beater bike is one is free from worrying it. It's hard to ride a new bike on winter salted roads. It's hard to take apart the bottom bracket of a new bike just to see how it works. But with a beater bike one is free to do just those things. So I don't consider a beater just an inexpensive bike, although they usually are.
For a low budget bike all I can think to tell you is this one sign I saw years ago. It said: "Pick two of the three below... Time, Money, Quality" One can never get all three. So with a low budget bike price is chosen, leaving time or quality. If you want it now, then you go to Walmart and get a lower quality bike. If you want quality, then you will have to be patient and search and wait for a good used one, which may take years to find. Just ain't no other way.