Either foam board or closed cell spray foam are the way to go. Either one has to be covered in an approved material to reduce fire hazard. I've had good success applying XPS foam board and covering with either plywood, gypsum board, or a stud wall with gypsum board. I've used all 3 methods on one basement depending on space and needs. If plywood or gypsum board is directly over the foam board, it can be attached with tapcon screws through the foam into the concrete. If a stud wall (if you want to run electrical or plumbing in the wall), a few tapcons with large washers can hold the insulation in place.

While some insulation may help, basements are always colder than the floors above because cold air falls. Are there registers and cold air returns in your basement? If there is a door at the top of the stairs, keep it closed. You might need supplemental heat in the winter if you're spending a lot of time down there.

We have good old fashioned pink batting insultation between the studs, covered with thick plastic. It works. Have thought about ripping it all out and replacing it with foam boards but just haven't gotten around to it.

Closed cell spray foam or foamboards is the way to go.

I built for years using Code approved fibreglass. Hate to think of what happened with some of those.

Credit: Building America

Worthy - that's my cellar!!