machka, marry me.

It is possible that you don't need to replace your rings (though given the condition of your chain, this is a long shot). If you use the same ring 90% of the time, it's very likely that you only need to replace one.

Be sure to replace the pulleys on the derailleur. I can't imagine that yours are not toast. It is not necessary to replace the entire derailleur. You can visually check it. My guess is that they will be very obviously and visibly worn.

Think of it like this -- when you ride in slop, grime in the road will get on the chain. You're basically applying grinding paste to the whole system. That it lasted as long as it did is a miracle.

Fortunately, none of these things is particularly complicated or expensive if you do it yourself. This is a great opportunity to learn how to take these things apart. After you've messed with your old parts a bit and figure out how they work, you'll feel confident installing the new ones.

One thing to be aware of if you ride in a lot of slop is to check the wear on your rims. Grime on your brakes can just chew up the rims and if they get too thin, that can be a safety issue. I just had to dump a set of wheels earlier this year because I'd worn them out.

That's your problem right there. The various "chain checkers" measure chain wear using a flawed concept and give very misleading results. Measure your chain carefully using an accurate ruler over a 12" (24 pin) distance. If the distance between 24 pin centers is less than 12-1/16" the chain is fine. If it's 12-1/16" to 12-1/8" replace the chain. If it's over 12-1/8" you will have to replace the cassette too and maybe sooner.

I'm a reasonably light (by current standards) 150 pound man who rides in very hilly terrain and my chains and cassettes routinely last 5000-7000 miles. I expect you are discarding perfectly useful chains and cassettes.