KeithL and Quickdoo have given excellent advice.
The made-in-china home hobbyist machines as sold by Harbor Freight represent the bottom level of quality in machine tools imported from China. You may get lucky and get an accurate, well-fitted, affordable benchtop mini-lathe, or you may get a $500 headache that you will sell asap. From the examples I've seen, examined, and worked with, you will likely get the latter. A brand name such as Jet and Grizzley will give much comfort when it's time for replacement parts or service. The next higher grade are mini lathes made in Taiwan, eastern or western Europe, and of course the domestic Sherline and Taig.
Important considerations for your bullet modifying projects are: spindle accuracy, repeatability of cuts, headstock accepts 5C collets. Accessories will include a steady rest, follower rest, drill chuck, and full set of boring, turning, facing, cutoff, and knurling tools.
You may consider a larger benchtop or lathe on a cabinet stand for your intended use in gun hobbies. A bare-bones used 12x36 Atlas can be had for about $500, and it is much more lathe than the mini you are considering.
Spending more on a higher quality machine will give more satisfaction in it's use and help the learning curve. There is nothing more frustrating than trying to learn and develop good machining technique on inadequate tools. When it comes time to upgrade, your better quality machine is more saleable than the economy job.
HTH
John