Early 1950s Singer, could be model 15; it came in various versions, regarding motor (potted/belted) , stitch length adjuster (knob/lever, lever=revers stitching). Other straight stitcher common in those years; model 66, 99 (smaller), 201. You mention model 33, but it's an industrial machine, not common for the home. Long bobbin models was still in production(128/127). I'm guessing not the most common either, though 128 was made until the early 60s. By the 50s they all had the same upper tension mechanism with a numbered dial.
Can you remember the bobbin? Was it round with or with out holes in the side? Slighly curved sides or flat? Long bobbin or round bobbin? Revers lever or a simple stitch length knob? Was it a drop in bobbin case (bobbin inserted horizontally) or was there a bobbin case you took out each time you had the bobbin out?
As far as I know the 400 series are very dependable machine, there shouldn't be any particular problem with timing. Any issues should be fixable and with lasting result.
I don't know much about the 600 series, but I have read here on the forum and elsewhere; some early 600 series were all metal, some had a few plastic gears. You have to check each machine because the exact same model turns up sometimes all metal sometimes with plastic gears. An all metal machine is a pluss, especially as the decades go by, but I don't mind plastic gears too much. They can last decades and can usually be replaced if worn down or damaged; These days replacements have better plastic material than they often used then.