The OP posted this under clarinets. Clarinets are pretty standard in terms of key placement, so not much difference. One thousand pounds should get you a pretty nice intermediate horn. Yamaha 450 (used), Buffet E12, Backun Alpha. Lots of choices out there.
If you have really small fingers, you should see if you can find something called a plateau clarinet. This is a clarinet that has all the tone holes covered, like you'd see on a saxophone. A couple Chinese companies still make them and there are some companies that convert regular clarinets.
Vito was the last "big name" company I know of that made them, so, student-class. Normandy clarinets were also pretty common. Those were Leblanc's intermediate models. There's one for sale on UK ebay right now. (Note that that one needs work.)
I've never played a plateau clarinet. Some folks have said that the plateau keys make the horn sound pretty stuffy, which shouldn't be an issue for you if you're a beginner.
A standard clarinet should be fine, and there are many very good second hand instruments in your 1K price range. Less risky is going to a store that has second hand stock for you to try a few, assuming as a beginner / intermediate, you already play to some extent. You may not get the bargain you might find on Ebay, but a good store with stock should have checked the instrument over by a technician. You should therefore avoid the shock of condition and repairs needed from an Ebay purchase. Which brings me to the point I am typing to make!
To respond to your comment about long thin fingers, you will notice on a clarinet that the upper and lower joint both have open tone holes, that when you cover the tone hole with your finger, a ring is pushed down.
Those rings close pads on tone holes higher up the instrument, and whether the rings are actuated enough to close these auxiliary tone holes depends on individuals' fingers. A thin finger may not push the ring down as far as a fatter finger. This is all no problem if the clarinet is adjusted to your finger, which is easily achieved by bending the keys as needed to correct the timing of the auxillay pad covering its tone hole at exactly the same time the finger pulp covers its open tone hole.
A good shop with a technician would be able to make sure adjustments that are needed for each player are attended to. Everybody's hands are different, and anyone who gets a clarinet new to them should be aware that trill keys, left little finger touch piece height, and ring keys are all fair game for adjusting to an individual for best response.
I would just go with a standard student model clarinet for a beginner.
As a retired music teacher (for a time I was the "woodwind specialist" for a local school districts instrumental program) I started many 4th grade (9 or 10y/o) students on clarinet.
Kids that age can be really tiny...with little fingers.
They can all do it. I never had a student that-practiced not be able to be functional.
The problem with little-finger-syndrome (lol) occurs when a student begins to use the right hand on especially the last two finger-tone-holes.
(If you notice, those are the largest finger holes to cover.)
I always found it best to experiment with the position of the right-hand thumb position.
Ideally one would want the "pad" of the finger (the part on the opposite side of the nail) to cover the tone hole, not the tip, as the tip of a finger is smaller/pointier..... Adjusting the right-hand thumb position can facilitate this.
I hope that this helps.
thanks for all the advice, especially about adjusting the rings over the tone holes. I shall continue the journey. Coming from sax, clarinet is a real mental workout, coping with the 12th difference in registers. Might help keep the brain in shape!