I've acquired a Series 3 petrol, first registered in 1972 (K reg) - it's in generally pretty good condition and has had some money spent on it by previous owners. It's has a curious anomaly (as all old Land Rovers undoubtedly have!) in that the chassis/VIN number (starts 241...) appears to indicate (according to Calvin) that it dates from 1963 - 1966, but for the most part it's a Series 3 (dashboard for example).

Anyway, i'm not a mechanic (but am keen hah!), and having driven it around a little, the engine appears to have some (hopefully) small issues that I can attempt to sort out....

- It is a bit tricky to start when hot or cold - it will go eventually but sometimes the starter motor just turns over and nothing happens - this can go on 2 or 3 times before it will go (but when it goes, it is not hesitant, it comes to life quickly).
- Once going with choke out it runs OK - however, when I push the choke in after a few minutes driving, it will sometimes lose power on acceleration and will misfire (sounds like a hissing noise). This is noticable on inclines when extra oompf is needed.
- With the choke fully in it has also stalled occasionally at junctions giving me a bit of heart attack...
- After this misfiring and stalling, I have taken to leaving the choke out a small amount and she will then run OK and doesn't misfire or stall.
- It has trouble idling when the choke is fully in, even when hot and sometimes will stall - I guess this is the cause of the stalls at junctions
- It smells as if it is running quite rich - very petrolly and fumy, but no excessive smoke.

It has a Weber 34ich carb and the ignition system appears to be quite new: new coil, new solenoid, new fuel pump, new distributor cap and leads. I have not checked the spark plugs yet (they look recent) but that was going to be my first port of call...

All of the above points in the direction of ignition or fuel/carb issues (I think)... but any advice greatfully received, particularly about where to go next. Reading suggests not fiddling with the carb until ignition is OK....

It does sound like there is some sort of restriction in the fuel supply.
When you pull out the choke you get more draw/"suck" [trying to keep this basic so you understand] pulling fuel in but the air supply is also cut down. Result engine runs rich but not as rich as it would when running normally with choke out.
With choke in you are likely running on the lean side so when at idle with less "draw" it cuts out.
The Standard Zenith 36iv carb has a little filter at the inlet to catch stuff. The Webber carb often came with a little in line filter.
The carb looks pretty new so either it has a bit of a blockage or it does not have the right set up/jets for a Landy.
Here is an old trick to clear a carb jet you can try.
Remove the air pipe so carb top is clear.
Get engine running and have choke in/off. Get the revs up some on the throttle lever on the carb.
With your other hand slap it down on the carb inlet [ don't worry it will not be sucked into engine ]
As engine slows remove hand and do the same a couple more times.
The sudden extra draw can pull crud away.

Thanks @tottot for the possible explanation. That gives me something to work towards. I will try what you suggest and see if that helps, if not, I may try to clean up the carb with a refurb kit as it seems a relatively straightforward process... I need to cut my teeth on something!

And yes, the addition of an inline fuel filter is a good idea - I've seen them in the hundreds of pictures I've looked at!

An in line filter needs to be placed away from the hot parts of the engine, many are mounted next to the carb which is poor as they get heated and cause problems.