When first DD was born (she's 13 now), my mother said the Godmother had to buy the christening outfit, so my girlfriend and I went out and she picked out the dress. Now when DD #2 was born (she's now 8), my MIL wanted to buy the dress, but since my girl friend was to be her Godmother too, I just said we were going to use the same dress. When DS came along 5 years ago, my cousin went out and picked up a christening suit for him. (His Godmother.)
When DD#1 was ready to receive Communion, MIL insisted on taking her shopping for her dress. Her reasoning being since she didn't know her when she was a baby (DH and I met just before she turned 2) and this was her 'first' grandchild and a grandaughter at that, she wanted to take her shopping. Oh, DH is one of 3 boys in her family, so MIL never had any girls to take out shopping. I'm sure if she was still with us today, she would be taking DD#2 out in the next few weeks to buy her her Communion dress. DD#2 will wear her big sister's dress from 6 years ago.
Now when DS receives Communion in 2 years, I guess I will ask my cousin if she wants to come with us to buy a suit for him. If she offers to pay for it then I'll let her, but I wouldn't insist on it. (Even though I know my mother would say she's suppose to buy it. )
Do what you are comfortable with. It looks like each family has it's own traditions on the subject. There's no right or wrong way to go, and I don't recall there being a set rule for it.