Prepositions are really difficult to understand in English...
1 used to show who is intended to have or use something or where something is intended to be put
There's a letter for you.
It's a book for children.
We got a new table for the dining room.
This is the place for me (= I like it very much).
9 used to show a reason or cause
The town is famous for its cathedral.
She gave me a watch for my birthday.
He got an award for bravery.
I couldn't speak for laughing.
He didn't answer for fear of hurting her.
1 in the direction of something; towards something
I walked to the office.
It fell to the ground.
It was on the way to the station.
He's going to Paris.
my first visit to Africa
He pointed to something on the opposite bank.]Her childhood was spent travelling from place to place.
1 used to say where something/somebody is or where something happens
at the corner of the street
We changed at Crewe.
They arrived late at the airport.
At the roundabout take the third exit.
I'll be at home all morning.
She's at Tom's (= at Tom's house).
I met her at the hospital.
How many people were there at the concert?source Oxford Dictionary
Nas sentenças que você citou"for" dá a idéia de propósito "purpose": I got a football for
Quando houver uma idéia deste tipo use o for.
O "to" e o "at" tem varios usos como for, mas inicialmente podemos memorizar o to
como "em direção a..." e o at
como "junto a...." Depois você memoriza as outras.
Ex. He works at an important company.
They are going to the beach.
Gostaria que mais alguém pudesse esclarecer melhor...