Caveat: I've only made cheese cake the traditional way, in the oven. That said:
Classic (NY style baked, which is what your picture looks to be) cheesecake is made with Philadelphia cream cheese, which is available in our Coop, so I assume it is part of their standard line.
Lidl has a cream cheese of their own line, it's pretty good. I think I remember Aldi has one as well.
You can use any full fat cream cheese.
Lately I have been using a recipe that uses half ricotta and half cream cheese - I prefer this, but the texture is a tad more crumbly.
To make the crust, graham crackers are not so easy to find out my way so I use any digestive or plain type biscuit (cookie), available in any cookie aisle here. You want one that isn't sweet. If your biscuit is sweet-ish, cut down on the added sugar. If you want to do something different you can use a flavoured biscuit, chocolate or ginger or cinnamon. You can also do a crust with finely ground almonds, but you will probably need to add a little flour to bind it.
I am of the opinion that a good vanilla and fresh lemon is really all you need to a make a great basic cheese cake; I grate a vanilla bean or two directly into the mixture, grate a lemon rind.
You can also add (real) almond extract to the cheese mix.
For other flavours, I prefer to add them in as a swirl - i.e., lemon curd, fruit preserves, etc. And of course, fresh fruit as a topping.
If you want to add flavouring directly to the cheese mixture, Etter's liquor (Cherry, Strawberry, or Winter Plum, Apricot, etc.) work. 15% alcohol, and you might need to adjust consistency to account for the added liquid. But as above, I prefer to make a plain cheese cake and add a fresh fruit topping, marinading the fruit in Etter Liquor first.
I've experimented with cocoa and espresso powders to make a coffee cheesecake; I think I added too much espresso, as it was overpowering. Worth further experimentation, as a mocha cheesecake is mighty good. With both cocoa powder and espresso you might need to adjust the sugar.
I've not done a caramel cheesecake...
Good luck - I'll be interested to hear how the cheesecake comes out using the Instant Pot.