Using the word "whether" instead of "which"

Solution 1:

Just as where is the wh-word that goes in front of questions about location, whether is the wh-word that goes in front of yes/no questions when they're subordinated:

• Is he going (or not)? ~ I wonder whether he's going (or not).

Since yes/no questions imply a binary choice, a conjoined or not phrase may often be added.
For the same reason, embedded question complements headed by whether can often use if instead:

• I wonder if he's going (or not).

Unlike other wh-words, whether is never used to mark a regular question:

• *Whether is he going?

because yes/no questions already do that without a wh-word.

• Is he going?

In this case, whether can introduce two conjoined infinitive clauses

• whether for me to buy sugar puffs or whether for me to buy coco pops

reduced by conjunction reduction by deleting the optional boldface above, to

• whether to buy sugar puffs or coco pops

So it's fine provided it is introducing a yes/no question or some binary opposition.

Solution 2:

You seem to have grasped the usage quite well.

The following two sentences mean exactly the same thing:

1. I must decide which to buy: sugar puffs or coco pops.

2. I must decide whether to buy sugar puffs or coco pops.

Solution 3:

Which is the clear favorite if you have more than two choices or if you do not want to list all of the choices. As other answers note, whether implies a binary choice.

Imagine you are going to get a kitten, and you get to pick from a litter of nine kittens. Which sounds better?

I don't know which kitten to bring home.
I don't know whether to bring home the white one, or the spotted one, or the calico one, or the runt, or the tabby-looking one...

The first is unmarked, the second means that you are violating Grice's maxim of brevity (and are therefore communicating something in addition to your hesitation at choosing).