Modern red dot sight options are terrific if you don't suffer from astigmatism...
For an RDS on a beater rifle you'll want light, small, smooth profile (snag-free) and tough. Just make sure you get one of the tube-style enclosed units so you have less issue with weather obscuring the glass and snow/debris on the emitter (i.e. not a "pistol-style" RDS, I don't know what the different styles are called).
There are a few good options out there in your price range, but most will probably steer you towards Holosun or Vortex. Some models only have one mounting option that I think will put the tube unnecessarily high above the receiver for your rifle.
For a lower budget option there's the Bushnell TRS-25. It's surprisingly well-liked despite the low price. You could always try it and sell it for a small loss if it's not up to par for you.
I put a Vortex SPARC Solar on a bush rifle, and I'm very happy with it so far. I really like the shake-awake feature. I didn't think it was necessary when I was shopping around, but now I won't consider an RDS without it now that I have it.
Are you sure you need iron sights? A QD mount for your RDS will probably be costly if it has good return to zero. Added to the cost of quality iron sights themselves... You might consider skipping irons and just mount an RDS. Current options in your price range have incredible battery life, auto-off, shake-awake, and dead nuts reliability... Irons are a lot less relevant.