In most of the cases, the phone interview contains a mini case led by the HR person. However, I heard the stories when it was just a fit interview.
If you have 0 case experience - try to get at least 2-3 weeks to prepare, otherwise, the chances of failure are high.
Re coaching question - depends on how many sessions you want to take. If just one - honestly, it makes sense to practice on your own first and after that take a coaching session.
If you are up to many session - get the basics in a couple of days and then go for professional prep. You can check my program in my profile - I usually follow it with my candidates.