If price is truly a factor, which you said it is, I'm casting another vote for the RAT RC-4. The size is right in what you said you wanted, you can get it in plain edge or partially serrated, and it is about 1/16" thicker than the RC-3. It's also made out of 1095 carbon steel which can take a beating and is easily sharpened.
You also mentioned "drag in the mud and use in any environment," so I again point to the RC-4. It has a coated blade that will greatly increase corrosion resistance. Yes, the edge is exposed and can rust, but if you keep it at least moderately clean in the field I haven't had any problems with mine.
Also, it comes with a very versatile kydex sheath. If you are indeed going to drag it in the mud, this is a lot easier to clean than a leather sheath.
They also have a "no questions asked warranty" that covers everything outside of normal wear from usage (including rust, so again, try to keep it at least moderately clean).
That all said, they have every size from 3-7 inches should you not want the 4 inch. Go here
www.knifeworks.com, and check out RAT Cutlery as well as Ontario Knives (a joint effort). Some of the Ontario versions come in D2 steel, which is another good choice, although it is a bit harder to sharpen as the steel is harder overall.