Boarding prices vary greatly depending on location, type of board (full pasture, partial turnout, or stall board), and the size of the facility. Not everyone is reasonably priced either. As far as classes, do you mean showing or lessons? Those prices will also depend on location. A lot of trainers I know do private lessons for $35 per lesson, I ask for $30. Group lessons are generally cheaper but you don't get as much one-on-one instruction time.
I pay $180 a month for an indoor stall and access to all arenas and pastures, but since it's so cheap I have to feed and muck out the stall 2x a day. It would be $230/month if I didn't do that. I pay $30 for one hour lesson.
At my barn it's about $350 for an outdoor board with hay, you supply your own grain, it's about $650 for indoor board, with everything... grain, booting, holding for vet/farrier, blanketing etc. And training board $1000 with all of the indoor board things but, training 5 days a week as well. All of this is the Canadian dollar by the way. And for me a lesson is about $75 private and $65 for semi private. And what I pay, is actually quite expensive you could find a much cheaper board if you look in the right places!! But sometimes it's worth it! At my barn it's definitely worth it!!