I don't know who chose him, probably a combination of the casting director and Lucas.

David Prowse was tall and imposing and the movie sets that the character appears in were shot in the UK, and he is English.

He did a series of short road-safety 'adverts' in the UK in the 70's - he was the "Green Cross Code Man" - where he had to wear a super-hero costume, stand tall, make obvious body-movements and gestures to teach kids to cross the road. Perhaps this role, whilst not 'serious acting' as some people would see it, showed Lucas that he had the skills to carry out the role of the expressionless Vader.

As for your 'important role' point, it was clear from the outset that they always planned to dub another voice onto the character. David Prowse has a regional west-country accent, more in keeping with a farmer than a galactic overlord. What they needed from him was someone with that physical presence, with some acting experience, and who would not be too expensive.