Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
First off the most important thing to know about Ryze is that you shall ALWAYS play very passive. Don't ever try to attack atleast 1-2 if your ultimate is not yet ready, though depending on how much hp they have.
About the Item Purchases:
Buying Health Potion is very optional, I usually don't ever buy it because I don't consider it neccessary when playing very passive. Then you should always buy Rylai's after buying Mejai's, that will make you much stronger healthwise, but also give u an additional AP boost. I suggest when going for Rylai's you buy Giant's Belt at first, then you choose on your own what way you want it.
After buying Rylai's just follow the order of item purchasing, when it comes to the last item. Depending on how well you're doing in-game after buying the items from AP book to Rod of Ages, you might decide on your own which of the items Guardian Angel or Lich Bane that you consider neccessary.
That's all from me, and please let me know how this build works out for you in the longrun, and remember to ALWAYS play passive when you decide to kick som butts with Ryze!