I think you need to find out a lot more about lathes and accessories before you even consider buying one.
Rather than a lot of posts with specific questions on this forum, it might be a lot easier if you visited a local woodturning club, went to some demonstrations (wood, art & craft shows etc) or spent a bit of time on YouTube looking at some basic turning videos and explanations of lathes and accessories.
In answer your question about a "point", that could either be a centre in the tailstock (lump on the right hand side) or a drive centre / prong in the headstock (lump on the left hand side, usually incorporating the motor). These would be for spindle turning i.e various shapes of cylinders such as stair spindles.
For things like bowls, you need other methods of holding your stock (wood) such as chucks, faceplates etc.
Hope this helps but find a turner, do a Columbo impression and ask a load of daft questions (no question is really daft if you not know the answer) and then think about a lathe, turning tools, chucks, faceplates, grinders, jigs, face masks, finishes etc. A lather is only the start!
Good luck.