In reply to Removed User:
The older mountain bikes used to have mounts for racks, but not many of the modern ones. Most child seats don't need special mounts.
Unless you are heavily loading the rack, you could use 'P' clips to fix it to most hardtail mountain bikes.
I use a 6year old specialised rockhopper, it's got mounts for a rack and is well suited to the hamax child seat. I'd look for secondhand, then save your money for the child seat, helmets (their heads grow), a double trailer (you might have another child), balance bikes, tagalong bikes, isla bikes etc, etc.