I'm not sure, but it seems to me that your form and its names are correct, but that your logic is slightly flawed.
The first time you load a page with this code, the category variable will not be set. This leads to an incomplete action in your form. That means that the first time a user uses the send button, the category variable will be empty.
After the first press wanted_category is set, and using the send button from now on will also set the category variable.
If this is not the problem, that is you that the first time you enter the page the category variable already set, then try writing out some variables and specify exactly what it is that is not working.
The logic is that when first time user comes in the page no categoy should be set and user will see all hotels. If user set a cetegoy by the form the page must show only the hotels that belongs in this category.
