I don’t know if it counts as cheap, but a Lee classic cast will do what you want. Great all around press.
This is what I use. Catches primers in a vinyl tube. I use it to decap all kinds of filthy cases. A friend shoots a lot but doesn't reload and he let's me pick up his brass on his private property. Some of the cases are partially filled with dirt. I soak them in a bucket and rinse and decap, residual dirt and all. The Lee press works great for me.
--HC