If you want to fork out for a couple of paid stalks, that's one way to test out whether this is something for you and as you haven't got a rifle, the estate can lend you one. You can also speak to the stalker about how they started out/kit they use/fieldcraft required etc. If you decide it is for you, ask around see if there is any other form of permissions going in your area. If there is nothing in terms of deer, then vermin is a good start and would justify a .22, .223 or .243.
On courses, the DSC1 is a good starter for 10 that is often recognised by many important players; namely, landowners, syndicate members and firearms departments. Doesn't necessarily turn you into a world-class stalker overnight but it shows a level of commitment to personal development in the subject matter.
And as you don't have any Section 1 rifles yet, you may want to think about joining a rifle club locally and doubling up on the reason for an FAC.