"Ich würde das gern kaufen" is a wish, but you can't affort p.e. the dress. "Ich möchte das gerne kaufen" is a request to a seller or a decleration of intent.

i think ich wuerde das kaufen means that maybe you dont want to buy it but for respect or being polite, you will show someone that you want to buy it. ich moechte das kaufen means that you really really want to buy it not caring about other things.

Ness is right if you're talking to someone else about your wishes and plans. But in practice (i.e. in a shop), you can use both and it doesn't really make a difference. "Ich würde gerne" in this case is just used to make the request polite.