Learn English – phrase(or a metaphor) that describes a person who has a restless mind

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”.

Even a blind squirrel finds a nut once in a while.

A blind squirrel has no practical option but to keep searching for nuts in spite of its natural limitations. The phrase is often used by the skillful to disparage the lucky breaks of others, but it is also used by the skillful to point out that luck played into their success. Just as persistence and luck intersect in real life, the blind squirrel proverb intersects with the motivational mantras:

Persistence overcomes resistance!

or

If at first you don't succeed, try, try again!

The blind squirrel proverb lands closer to the expression of:

sheer luck

The motivational mantras land closer to the expression of:

try your luck

or

ride your luck

The following are not idioms per se, but they turn a good phrase for the intersection of luck and persistence:

“Diligence is the mother of good fortune.” Miguel de Cervantes Saavedra

"Luck comes and goes; you have to seize it." Jean Van Hamme

“I didn't wait for Luck. I tore after it with a truck.” A.A. Bell

“While persistence offers no guarantees, it does give 'luck' a chance to operate.” Tom Shippey

“Trust your luck, Taran Wanderer. But don't forget to put out your nets!” Lloyd Alexander

“Luck is distributed at six in the morning” Luis Zamarro Fraile

“A trifle can be enough when luck is on your side.” Margi Preus

“As regards the extraordinary prizes, the element of luck is the determining factor.” Theodore Roosevelt

And the following quotes turn a good phrase for the intersection of persistence and success:

“Eighty percent of success is showing up.” Woody Allen

“Fortune sides with him who dares.” Virgil

“Success is stumbling from failure to failure with no loss of enthusiasm.”
“Kites rise highest against the wind...” Winston Churchill

“People who avoid failure also avoid success.” Robert T. Kiyosaki

“It is hard to fail, but it is worse never to have tried...” Theodore Roosevelt

“There is no failure except in no longer trying.” Elbert Hubbard

“The road to success is dotted with many tempting parking spaces.” Will Rogers

“Develop success from failures. Discouragement and failure are two of the surest stepping stones to success.” - Dale Carnegie

“Don't be afraid of failure. This is the way to succeed.” LeBron James

“Our business in life is not to succeed, but to continue to fail in good spirits.” Robert Lois Stevenson

The intersection of these ideas seems to be a popular theme, so if you persist in your archery word picture, you may have stumbled blindly onto an idiom for the future.

Shoot enough arrows, and you may hit a blind squirrel.

or

Even a nut might hit the bullseye.

Or some combination of the two ;) I'll give you a one week head start to register a trademark!