You can get into vet school with both A Levels and BTEC. Its one of those careers where experience is really important, if not more important than your subjects. Doing the BTEC will allow you into virtually any animal based career, vet, zookeeper etc. A Levels will keep your options open, but if you know Biology and Chemistry bores you (which is what you will need to study to be a vet if you go via A Levels) I suggest you pick the BTEC. History also leaves doors open to you if you do decide you want to go down a humanities route and you can do History alongside Chemistry and Biology which makes even more pathways open to you.
At the end of the day, pick what you feel is right. You have the whole of summer to think on it and decide.