I have a few rain coats. Two that are less than $100 are the Marmot PreCip and a ECWCS gore-tex hooded shell. Both are excellent coats for most uses and the military model is probably both cheaper and tougher than the Marmot. I have a gore-tex military coat in woodland camo that is ten years or more old and works very well. You can get them online inexpensively, say from $35 to $80 most of the time.
When I went to Alaska last year Caribou Hunting I searched EBay for a couple months and found a Columbia jacket for $39 and it worked great as we were rained on 9 out of 11 days North of the Brooks Range. Just put in a search of brands you would like and the size and within a few months you will have a quality jacket at a affordable price. Mine even came with the tags still on it as new.
Got to agree you need to narrow parameters. For something packable and used sporadically the Marmot is great. The military goretex is bulletproof and fairly cheap. For everyday hard use, Helly Hanson seems to be very popular.