A phrase that means "to finally select (or decide) something"

Solution 1:

A word mentioned in the question is suitable: settle (sense 7, “To determine, as something which is exposed to doubt or question; to free from uncertainty or wavering; to make sure, firm, or constant; to establish”). You can say, “I settled upon the fourth alternative”. In my mind, settled upon may indicate slightly more thought about the alternatives than would use of picked or chose. Also consider aforementioned selected and decided on or upon. [Links and definitions: en.wiktionary.org.]

As far as idiom goes, I don't know of one comparable to “ostanovitsya na / to stop on something”. One might say, “I took X home to mama” / “My take-home was X” / “I hooked up with X” to express choosing X with more thought or less. Those are all more figurative than idiomatic but are informal and readily understood.

Edit: ezpresso's comment reminded me I left a link out. End up has a sense “to arrive, esp by a circuitous or lengthy route or process”. Eg: “I ended up with the fifth alternative” or “I ended up using the sixth alternative” or “In the end I took the seventeenth alternative”.

Solution 2:

I understand your question to be: "What word/phrase means choosing the best out of a large range of options?" I think "to hand-pick" works nicely. To me it elicits the imagery of being in a grocery store looking for apples. You're given many options, but you personally choose only the ones you think are best. http://www.thefreedictionary.com/hand-pick