Recommendations are going to depend heavily on the size you want and what you want to grow/stock--but cheapest is to go no-tech.
I have two planted vases in my kitchen that are pretty good examples.
2.5g with no filter, no heater and receiving only indirect light from a nearby window houses cherry shrimp, various "pest" snails, a nerite and a small school of male endlers. Plants are a variety of floaters, java fern, xmas moss, crypts, cardamine lyrata, 'sunset' hygro and 'bold' hygro. Substrate is plain ole polished aquarium gravel, hardscape is a couple river rocks and as big a chunk of driftwood. Waterchanges are plain tapwater, 20% weekly, vase cost me $2 at the thriftstore, everything else was pulled from my spare stock/other tanks.
3g planted vase on my counter has fluorite substrate, one large/one small piece of driftwood, planted up with frogbit, salvinia, hornwort, red root floaters riccia, 'sunset' hygro, 'bold' hygro, star grass, temple plant, crypts, dwarf pennyroot, xmas moss, and cardamine lyrata. Houses pond/ramshorn and malaysian snails, scuds, cherry shrimp and a breeding pair of hybrid endlers (offspring get pulled regularly). No filter, no heater, indirect light from windows 10+ feet away are supplemented with a gooseneck reading lamp ($20) and high lumen bulb ($8) for 6-8 hrs a day.