Hi Reg
Not a silly Q at all - a perfect fit is an absolute requirement - the chuck is a precision piece of kit. Which is why they are not cheap (There are nasty rumours about profiteering!, but the chucks are undoubtedly well put together).
Several routes open to you........
1 - You can do a lot with jam chucks - the name says it all! Cut an appropriate cavity in a softwood block that is mounted on a faceplate, and then jam your workpiece into it, and off you go.
A cheaper-than-a-chuck solution - I've done quite a variety of bowl type things that way.
2 - Or use a similar block turned and mounted on a faceplate, and glue your workpiece to it, using some stiffish paper as the meat in the sandwich. Ease/chisel your piece off when done (sounds a bit primitie but can produce v v good results.
Same again - works a treat.
3 - or indeed go for a chuck. Any chuck will do the job, i.e. to hold your workpiece securely. There are - broadly - two types, a collet chuck and a scroll chuck.
Folk often mount the piece into a collet chuck off the lathe cos it's easier to handle that way. Some folk swear by them, some folk find them too fiddly, but they do the job.
The Scroll chuck is set-up to work in such a way that you'll probably never need to take it off to mount a workpiece - e.g open jaws, insert workpiece, close jaws.
You pays your money and takes your choice - collet chucks start at about £40 (I think!) and rise to £100 or more new. Scroll chucks start at about £90 and rise to over £150 new.
They do indeed screw on, at the headstock end. Your drive shaft, where the centre currently sits may have a 'thread protector' fitted - that's a large nut that protects that shaft thread by covering it up.
So to fit them, take out the centre, take off the protector if fitted, and screw on the chuck.
Your lathe docs will tell you the thread size - and therefore the chuck threadsize needed - that you need to get right otherwise it won't fit!!
It'll look something like 3/4" x 16, or 1" x 8 - the first is the shaft size, the secnd is the teeth per inch (TPI). The chuck and shaft dimensions must match. Adapters are available and usually work fine.
Happy hunting! Prices on Ebay for this kind of kit tend to be between 1/2 and 3/4 of the cost new.