I'm in the process of making a whole section on his ult but I can give a quick snapshot for the time being.

You can use it for scenarios such as cornering a target, getting over walls, moving minions around, or to take your team into a fight. Deciding when to use it can be slightly tricky as it does have a channeling time before the teleport. There are times when you use it to just teleport past your target to get a kill or one person takes it and another keeps walking towards your enemy to corner your target. Timing on the ult gets better with practice and if you feel like there never a good time to ult that is not usually the case. Its more of the fact you don't know how your team is gonna react to the ult. Don't be afraid of using it and messing it up, it happens.

Ghost is a great summoner on Ryze without a doubt. It is great for chasing and escaping but doesn't offer much more than a self summoner. Id use ghost in certain matchups where you need the chase potential.

Heal on the other hand gives us a lot more flexibility. We can use it to gain a burst of movespeed or to heal ourselves. The most important aspect of heal though is that it target another ally. Since Ryze is so prone to being ganked early your jungle will most likely also be present. This helps both of you either secure a kill or if your jungle messes up the gank you can save him with heal.