Christopher, your goal is realistic and your intent is correct: you do wear a "rain layer" over your down as part of a layering system. There are many rain shells of various designs that will meet your needs and the basic "trick" is simple: you get one that's sized to fit over your insulation layers, rather than just over your "tee-shirted shoulders", for example.
The variety of rain shells available to you range from really cool, ultralight products that experienced outdoorsmen (a gender neutral term in intent for my sisters in outdoorsnicity) are using to great effect as an outer layer alone and in combination with other layers, on down (in price) to somewhat heavier weight (and heavier duty) shells that others of us use. An exception to the heavier weight/duty but lower price pattern are the first ones I'll suggest you check out:
--DriDucks. These are "breathable" (uh....not really), super lightweight rain jacket/pant sets that you can get for under $40. They are cut large, intending that you put them over an insulation layer. They pack down super tight, don't weigh much and aren't very resistant to brush/twig snags, etc... but at this price, killer.
--Marmot PreCip. Available as pants and "tops", the jackets are in sale season right now and go for about $75 in adult sizes. This "breathable" product sheds rain, has pit-zips, packs down nicely, is reasonably light unless you're using the high-end stuff and comes in tall sizes if you need it. My family use this product and it performs very, very well in High Sierra rain.
--Uber-shells. Not a brand, but a whole variety of super-lightweight shells made by either boutique companies like Mont-Bell or tiny outfits run by gram-shaving, design-optimizing zealots. This is up out of my league, but there are plenty of people on this site who can (and have already) post reviews, photos and details about these products -- a few of which might beat your $100 threshold (several will not).
Finally, to reiterate what I think you know: your layer system will include components that you can wear separately or combined for different purposes. The rain shell is an essential part of that system. Happy Hunting!