Some things in life are taken for granted and you never think about them. For example you will spend a lot of time and money getting a really cool looking washing machine, and then 
put it in your basement, and not spare a thought for it until it conks off. The bath hamper too falls into this category.
You get one for $10 or $15 and use it for some time before you think that it is time to change it. You then go out and get one that probably looks exactly like the one that you already had for the same price. When you consider the bath hamper from a purely practical point of view, there is nothing wrong with this. When however you consider that you actually go to a lot of time to make your bathroom look nice why would you want to spoil the whole effect with something that stands out of place like a sore thumb.
This does not mean that you spend $50 on a bath hamper. If you fall in this category, you probably would not be reading this article in the first place. What you can do is go a little above your budget and get something that looks really nice for your bathroom. For example, for around $17 you can get the rectangular pop up baskets in white or pale cream that actually blends very well with most bathroom schemes. Since they are made of nylon there is no problem with dampness affecting them too.
Of course you can go a little higher and get plastic hampers and you get quite good ones for around the $35 range. Most of the time though this is really not required, unless you want something that has a large capacity.
You also get the rattan baskets that look really nice whether they are painted or not. If you like their look then there is nothing else that gives the same class, although you will have to pay more for it. As long as you air out your bathroom properly you should not have any problem with mould too. In any case all it takes is a few seconds to touch up any place that has lost its coat of paint and problem solved.