Get the min of one column but select multiple columns

If you are using PostgreSQL, SQL Server, MySQL 8.0 and Oracle then try the following with window function row_number().

in case you have one id with similar amount then you can use dense_rank() instead of row_number()

Here is the demo.

select
    id,
    name,
    amount
from
(
    select
        *,
        row_number() over (partition by id order by amount) as rnk
    from yourTable
) val
where rnk = 1

Output:

| id  | name | amount |
| --- | ---- | ------ |
| 1   | A    | 3      |
| 2   | C    | 18     |
| 4   | I    | 2      | 

Second Option without using window function

select
    val.id,
    t.name,
    val.amount
from myTable t
join
(
  select
        id,
        min(amount) as amount
    from myTable
    group by
        id
) val
on t.id = val.id
and t.amount = val.amount

In many databases, the most efficient method uses a correlated subquery:

select t.*
from t
where t.amount = (select min(t2.amount) from t t2 where t2.id = t.id);

In particular, this can take advantage of an index on (id, amount).

You did not specify your db vendor. If it is luckily Postgres, the problem can be also solved without nested subquery using proprietary distinct on clause:

with t(id,name,amount) as (values
 (1,      'A',          3),
 (1,      'B',          4),
 (1,      'W',          3),
 (2,      'C',          18),
 (4,      'I',          2),
 (4,      'P',          9)
)
select distinct on (id, name_of_min) id 
     , first_value(name) over (partition by id order by amount) as name_of_min
     , amount
from t
order by id, name_of_min

Just for widening knowledge. I don't recommend using proprietary features. first_value is standard function but to solve problem in simple query is still not enough. @zealous' answer is perfect.