Hello and welcome also from Carmarthenshire!
Not sure exactly where you are, but they are a very friendly bunch round here; last local TAS meet was in Feb, but you never know...

We're not far from Llandeilo and always happy to meet new friends.

We've kept chickens/pheasants/partridge and gardened extensively for years, but though I have some experience with bigger, more exotic critters, sheep etc. (next stage) will be new for me. Loads of advice on here though...
You can go down the poison route with the brambles if you want (glycophosphate type), but I'm not a fan of chemicals and usually just cut them back... very persistently! It depends on just how much there is, as much as anything, and how long you want to be working on it for. We have a brush cutting scythe, but a petrol brush cutter would make a good start. Do you have anyone you can call on for a 'working party' to get you started? There are plenty of people who can advise on here re effectiveness of goats/pigs etc with roots.
Angela