The first suggestion I would make is to use hand-ground HSS cutting tools for use with any of the light duty imported lathes, for typical turning and facing operations, on large or small workpieces. Carbide cutting tools aren't a solution or subsitute/shortcut for small lathe users. Most carbide cutting tools don't even have particularly sharp cutting edges.
I'm not a machinist, I'm just familiar with the small lathes from China and the issues involved with the low quality of finishing that these machines exhibit. I had a little previous experience from a 1 year high school machine shop class, and later set up and operated machine shop for manufacturing light duy machinery. More recently, I became interested in metalworking again, and started buying small lathes and associated tooling.
There are some tool dealers that sell pre-ground HSS cutting tools in sets.
3/8" set isn't appropriate for a mini-lathe, but I've seen 5/16" sets on eBay.. maybe some dealers have 1/4" sets, too.
All beginning small lathe users should familiarize themselves with tool grinding geometry as a starting point. Get a handful of HSS blanks to begin the learning process, and duplicate the grinds of the pre-ground tools, and also other configurations that might be needed.
Read the excellent Tool_Grinding tutorial by Harold Vordos concerning grinding wheels and procedures for hand grinding HSS cutting tools.
For general lathe usage, read some instructional info such as South Bend's How To Run A Lathe booklet, or some basic machining practices type books.
Another useful source of info is Shop Reference for Students and Apprentices available from Enco, published by the same company that produces Machinery's Handbook.
As Anorton pointed out, there are often quality issues with new small lathes from China. One can't assume that everything is snug and properly fitted.
One method that will show the user where problems are, involving fit and or adjustments, is to place a short bar (about 8") in the toolpost (simulating a long cutting tool) and apply finger or thumb pressure to see where loose-fitting dovetailed components are causing problems.
Any beginner should buy some easily machined materials to work with, starting out. Cold and hot rolled steel are cheap, but they aren't easy to produce good finishes with, as introductory materials. Choosing some leaded steel alloys will generally produce much better results. Choosing machinable grades of stainless steels will eliminate the frustration of trying to make parts from unknown grades of stainless/mystery metal. Some grades of stainless are very difficult to machine on small lathes.
Setting the cutting tool edge on the centerline of the workpiece (also the center of the spindle and tailstock bore) can be accomplished with a center gage that the user fabricates, or aligning the cutting edge with a dead center point in either the spindle or tailstock, or by using the steel rule method.
The steel rule method involves placing a pocket-sized rule beween the cutting tool tip and the outer surface of a piece of mounted round stock. As the tool tip approaches the rule against the round workpiece (or test bar), the rule becomes confined between two points, pointing in a direction that indicates if the cutting tool edge/tip is on the centerline. When the cutting tool is adjusted up or down, the rule changes position. When the rule is "perfectly" vertical, the cutting tool edge is located on the centerline. The steel rule doesn't need to actually be a steel rule, it can be any flat, straight, smooth piece of thin flat stock, such as a section of stiff feeler gage stock. A section of stiff feeler gage stock is actually better than a steel rule, since it's surfaces are completely flat, where a rule is partly covered with engraving.
Some users of small lathes from China will make a tall toolpost with a wide base that mounts directly onto the cross slide, eliminating the compound slide when they are just turning stock, and don't need the compound feed. This is a work-around to eliminate the extra flexing introduced by the compound slide.
It may be necessary to investigate many other potential quality issues with the mini-lathe, although it can get quite involved. The spindle bearing on my 9x20 model wasn't seated properly, and caused a lot of chatter, for example. There were various other problems that had a detrimental effect on performance with that model.
I doubt that the flex shaft-endmill will work, as the setup won't be rigid enough. The combination machines that I'm familiar with aren't capable of operating the mill and lathe simulaneously, as most of them only have one motor, and it's only engaged for one operation or the other.