When you talk about a polarizer, I will assume you are talking about a circular polarizer (CP). You should be aware that polarizers are like any other glass you will buy in photography - you get what you pay for and good and cheaper are not usually two words that I would use together to describe a polarizer. You should expect to pay between $130 and $175 for a good quality CP - if looked after properly, it will last a lifetime.
For your other question, assuming you are currently looking at screw-on polarizers, the ones that I have will not fit in the filter holder that I have for my Lee ND filters and GD filters. There maybe other "filter holders" that they will fit into, but remember they were/are meant to screw on to the front of the lens and not to be used in a filter holder.
Check this review out.
Tokina 12-24mm f4 DX Review - Complete "Hands-on" Lens Test . They note that a full thickness polarizer on the 12-24 Tokina will show a small amount of vignetting when used at 12 mm. If you can tolerate this (you can probably edit it out with a slight image crop if needed), then you could go for a regular CP as I do believe the slim ones are a little more $$ than the regular ones. There is also the question of whether you are going to purchase a coated CP - I would strongly recommend that you go in this direction. They are a little more $$, but if you can find the money, they are a better buy than an uncoated one. B&H sell a variety of 77mm filters, I believe that is what you lens takes...
77mm polarizing filters. HTH.
Cheers,
WesternGuy