One of my favorite topics, having grown up close to two apple orchards...
Most likely, by "quick-cooking," the recipe intends you to use a pie or sauce apple, i.e. one that softens readily with heat.
Sauce apples. Use these for a pie if you like VERY soft pie contents. Personally, I prefer applesauce that has some chunks in it, so I don't use "sauce apples" for sauce; however, the standard is to list for sauce those apples that practically dissolve (like McIntosh).
Pie apples. An apple listed for pie is typically one that retains its shape but softens well (like Cortland, Mutsu, Empire, Jonagold, or Fuji).
Consider the taste. Some apples (Gala, for example) lose a lot of flavor when cooked, and are best for eating raw. Others gain tremendous flavor when cooked (Empire).
Which apple to use is certainly a matter of preference. Some people like their pie apples to remain quite firm (using, say, Granny Smith), while others like them to be VERY soft (and thus use a "sauce" apple).
Here's some apple lists/charts ... I'd say look up the varieties readily available to you, and see which ones are listed for sauces or pies.
Look up the website for your local orchard - they may link to a usage chart for the apples they grow!
In his in depth review of pie apples, Kenji Alt points out:
Well, there's another thing that acid does: it strengthens pectin, the
cement-like glue that holds together the cells of fruit. So looking at
this arranged spectrum of apples is actually a pretty good indication
of how well each fruit is going to hold up during baking. The further
right along the browning scale, the firmer the apple should be in the
finished pie.
This same affect will apply to baking apples filled with cranberries: you want an acidic apple, as they are going to hold their shape best when baked.
While I don't know the varieties available to you, he points out that the more acid the apple, the more slowly it browns when cut:
[A]cid can inhibit the browning oxidation reactions that take place in
fruit flesh when it is exposed to the air. For this same reason, cooks
will store trimmed artichokes in acidulated water—it prevents
browning.
The slowest browning, and most acidic of the US apple varieties he tested was Granny Smith. This Whole Foods recipe for cranberry and almond stuffed apples concurs.
This goal of having a sweeter apple to counter-balance the cranberry filling is at odds with needing a more acidic apple to contrast with the cranberries.
Instead, you may be better served by adding sugar to the cranberry filling. Since both cranberries and apples are assertive flavors, they will stand up very well to a sweet filling.
Time and temperature for apples are pretty flexible. A survey of baked apple recipes shows options from 325 F (160 C) for about 45 minute to an hour to 400 F (205 C) for 15 minutes. The important thing is to take them out when they have become tender when tested by pushing a knife point through the body.
Best Answer
Looking through recipes suggests a variety of apples. Gala showed up the most, with Fuji in second, and McIntosh and Delicious tied for last.
If you want to go with the "source" of the recipe for Charoset, though, you'll want a sweet apple. The recipe has its roots in Song of Solomon/Songs, and the verse that refers to the apples reads as:
So, for authenticity, go for a sweet apple, but Gala is the most mentioned apple in recipes online.