Cost of neutering?

Roughly depends on the size of your dog, the larger the dog the more expensive the neutering will be. Also depends if your dog is male or female, the operation for a male is generally slightly cheaper because it is a shorter operation. Roughly it should cost between 100-150euro including pain relief and antibiotics, depending on your vet.
6 months is an average age, if you have a female you should really try to get her done before she has her first heat, which could be from 4-5 months onwards, it is medically better for her. It is a myth that a female dog should be let have one season or even one litter before neutering, it is medically unfounded and really just an urban legend. For a male dog 5-6 months is the best age, before they sexually mature and start doing things that male dogs do! If you get them neutered before they start this, they are less likely to have these behaviours than a dog which has already started prior to neutering.

I know someone who got two female pups neutered and the owner had a medical card and most vets have a thing if the owner has one then they'll do it at a reduced price but they only have x amount of spaces a year so they might be all gone.