I don't know about cheapest, but I would have to say either the Honda Rancher or Foreman 4x4 S models. Bulletproof.

 

Are you sure those are your priorities? Usually cheap and reliable dont describe the same quad, its one or the other. Theres a reason some quads are cheap.
Wouldnt work ability, ride quality, diff lock or not, auto or manual, irs or solid axle...and so on be more important? Once you have the cheapest one, you may end up hating it, and being unable to take the big drop in resale value, youll end up keeping a machine you hate.
The cheapest way to get into a 4x4 is the used market. Every year many like new quads come up for sale , which are perfectly good, and are at least a thou cheaper than new.
Any other priorities?

 

I'd try to find an old Honda 300 fourtrax. Those things seem to run forever.

 

He said 4 wheel drive not 3 1/2 wheel drive.

 

Yeah you're hilarious. Show me an ATV more reliable than a Honda.