I am looking for a cheap solution that offers full internet usage on my TV (basically, I want to use my TV as a monitor).

I have looked briefly at Mini PC's, Google Chrome Cast, and Roku type devices but information is vague.

I want to be able to view any site, with any content, on my TV without restrictions. I originally thought I may go with a cheap tablet or laptop but if anyone knows of a specific product that may work, I would appreciate it.

You have missed out an important factor, COST.

For a fuller web experience a mini pc or laptop would be in order.
The other options give a cut down version of web pages due to encoding.

Also it depends on the technology built-in to the particular make/model.

Any specific suggestions for a mini pc?