The same symptoms came with a house we bought a few years ago. Turned out that the house had a septic tank (in the middle of a residential community with sewers). We pumped out the septic tank; but improvement was only brief. Finally I found a sewer contractor who understood sewer lines. He found that the pitch of the line from the house to the septic tank was less than it should be (line was too level) and that caused slow flow and frequent clogs.
It's relatively easy, of course, to snake the lines and the vent pipe; so check those out thoroughly. I don't see how a new toilet will make anything better, however, if the problem is in the pipes somewhere.