It may seem like a good idea, but you live in Germany, so can forget about sensible air rifle usage.
If you want to buy one freely it will be limited to 7.5 joules (5.5. fpe). I've got pistols more powerful, and they are only good for punching holes in paper at 6-10 metres.
In the UK we can freely buy rifles up to 12 fpe. In Germany you can't.
Air gun laws - Wikipedia, the free encyclopedia
Air weapons exceeding 7.5 J muzzle energy, e.g. field target guns, are treated like firearms and therefore require a relevant permit for acquisition and possession. Proof of need, a clean criminal record and the passing of a knowledge and handling test are required to gain the permit.
Presumably this wouldn't be a problem for you, so fill your boots.
AFAIK you will not be allowed to use one for vermin control. Targets only.
Rabbiting and ratting, also grey squirrel and pigeon, with a 12fpe air rifle is often the introduction to fieldsports in the UK. But not allowed in most of Europe. Certainly not France, and also I think Germany.
As said "packing a punch" at 50 yards plus is not possible with a UK 12fpe rifle, we would need an FAC rifle in 20-30 fpe, which realistically means a precharged pneumatic rifle.
Which are expensive. To buy new, with decent 'scope, refilling kit (dive bottle or pump) could easily cost over £1000.
A good quality springer will start at £200 plus new. The best are made by Weihrauch (DE) and Air Arms (UK). Their better rifles will be £350 plus, then there will be a 'scope and mounts needed. Another £200 for anything decent.
you could start with e.g. a Turkish Hatsan or Webley break barrel and cheap 'scope. £200. Or even a Chinese SMK. But you might soon regret it.
Air rifle practice is very useful, particularly with a springer, which requires a firm consistent hold. You don't need to practise at 50 yards plus, 10-25 yards is all that is necessary, with suitably small targets, and .177" pellets. Even an emasculated 7.5 joule German air rifle at 6-10 metres will deliver useful practise, and you may be able to set up an indoor range.