It looks like that lathe comes with a drive centre (the thing with spikes), a faceplate and a set of collets. That ought to get you going in the sense that large enough diameter work can be driven by tthe drive centre so long as supported by the tailstock (to keep it jammed on the drive). The faceplate allows you to mount stuff on it.. it often takes some ingenuity such as mounting a timber former on there to hold and drive the work or directly screw into the work from the back, or glue etc. It gives you access to e.g the inside of a bowl or the front of an eggcup. The collets will hold small cylindrical objects and have less of a crushing effect than a chuck would. It depends how 'flexible' they are from the viewpoint of the range they can clamp effectively i.e if a 6mm collet can grip a 5mm rod or only down to 5.5mm say. You often have to get creative and ,say, turn a sacrificial spigot on one end to hold a part or make allowances to cut off the end with drive spike holes and hand finish …
You can always buy chucks later but they're going to be more for gripping tougher stuff than your soft material or gripping a holder you made specifically for a job.
For sanding, well usually the work is allowed to revolve and the paper applied either attached to sticks or small bits held such that they can pull out of fingers rather than pulling off fingers if there's a snag.
Additionally you will need some lathe tools:..chisels and gouges and a way to keep them sharp. I have no idea how good the chisels proxxon sells are. there's going to be a learning curve here anyway specially in sharpening and honing your tools.