Could this also mean "a chair" in an indefinite way or should I use "một" even in this situation, where I don't want to specify a concrete number?
If you want to express the concept/object in general, just skip the classifier: chair(s) in general is/are simply ghế (plurality indicated by adding những or các first). If you want to be really specific, you must use the classifier 'cái/chiếc' and it becomes very often 'the' in english. If you need to be unspecific but also not too general like in the first example, say 'một' + classifier 'cái/chiếc' + noun 'ghế' f. ex. and you'll get 'a chair'...