In general the order matters to some extent. Consider the following:
Ask for money.
Ask your mother.
Ask on Tuesday for money.
Ask for money on Tuesday.
Ask your mother for money on Tuesday.
Ask your mother on Tuesday for money.
On Tuesday ask your mother for money.
Ask your mother for money.
Ask for money from your mother.
All the above are understandable.
The last form is rather ambiguous, you could be asking your brother to give you money that came from your mother. The penultimate sentence is preferable.
So, most often, You'd place the recipient of the request earlier in the sentence than what is being requested. Usually the recipient of the request would be first.
There are definitely preferred orders for sentences of this form but I don't know of any firm rules.