As others have said, Hardware steel is definitely gummy and will give you a poor finish - as will most 1018 bought from a steel yard - although you can work with the latter if you have a really sharp and honed cutting edge.
You show one photo with wavey marks in the finish. I have had similar results when thin diameter work protrudes out to far from the chuck. I think the rule of thumb is support all work extending over 3 diameters from the chuck. So 3/4" OD round stock - hold the end with a Live center in the tailstock for any length over 2 1/4" . Makes the work much more rigid and produces better finish.
The other thing to try is sharpen your HSS tool bits periodically, including touching up the top(chip breaker area). And manually run the cutting edge over an oil stone. Also round off the pointy end with a small radius - (1/32 to 1/16" r) to insure the cutting tip doesn't individually score the work, leaving randomly deeper cuts. I took a close look at a couple of brazed carbide bits recently and learned they all have a tiny flat edge at the pointy end, causing a smooth finish with a flat overlapping cut, versus a series of tiny deep v cuts - that look and feel rough to the touch. So look geometry also.
LAST thing that might help. Put a dial indicator on your tool holder and watch the dial as you take a cut. The tool itself should be rock steady. If not, if the tool moves even .001" in and out during the cut, you have something wrong with the cross feed screw and the bit will produce deeper then shallower cuts - resulting in a rough finish. Maybe tighten up your cross feed thrust bearings. You have a new lathe, so wear likely not an issue, but it's very interesting to watch the dial indicator a couple of times to see what is happening with the tip of the tool.
Good luck. I am sure this will sort itself out with a little experimentation.
Glenn