There are so many different wood lathe projects out there, it can be a bit tricky figuring out which one you actually want to do.
The best engraving machine is worthless when you have no big project you want to do. One project you can do on the wood lathe is simply an ‘object’. By this you show off what you can do with a lathe as far as making different shapes and proportions, without really worrying about the fact that the object has no inherent use. This is a really good way to practice your wood working skills as well. Another nice thing about this it that your options are endless and you can have a lot of fun with it.
This object consists of a cylinder of wood that has been shaped into more or less a goblet shape. Make the bottom base and the top equal in size, and then make a triangle out of the top of it. Put a flat edge on the top, then taper it in for a bit so it looks a little like a cup, then make another flat edge along the inner cylinder, then taper it again to the thinnest point in the item. From there, expand it out to be the base of the goblet . You can use this area to put in different decorative swirls, expansions, swells, and other things.
After you have that set up, taper it out to the base of the object. If you want to make it into a goblet, then hollow out the inside of the top. You can use it to keep liquids in if you use the right varnishes.
Otherwise, you may want to look into just leaving it as a solid piece of work and using it to hold up books, show off your woodworking skills, or as a practice piece to see what different stains, varnishes, sandpapers and things like that can do to different woods. Have fun using your lathe and never stop using your imagination to make good projects.