“But also for enjoyment,” “but to enjoy myself, too,” — either could work You don’t have an error in the last sentence, but it would be better to say, “Professionally, I’d love to get one of the jobs I’ve applied for, teaching English to adults.” If by “for professional purposes” you mean that it’s for their professions, you could say “teaching English to adults that need it for work” (since you’ve already said professional in the sentence). If you mean that it’s for your profession, having already said it at the beginning of the sentence is sufficient.