I fished muskies for 42 yrs in western NY and western PA., casting and trolling, mostly Chautauqua lake because I live here. The rivers mentioned I am not familiar with. Spinning gear does have it's place in muskie fishing. IMO it's the best choice for fishing jigs/reapers, lizards, or pork, 1/2 to 3/4 oz. jig heads, dressed or undressed. Lakes or rivers, anywhere jigs are a good choice, what you want is a spinning rod about 7 ft long rated for 1/2 to 1 1/2 oz lures. I prefer mono, 15 lb maxima ultra green for fishing jigs. Jigs are great muskie lures especially for cold water. Some rivers are well suited to fishing jigs, some aren't. Along weed lines, around rock piles, drop offs, etc. spinning gear, jigs will work.
Bait casting is the way to go for all other casting applications. Rivers with a lot of brush where you're going to be fishing a lot of surface or shallow running stuff, most definitely bait casting. This reply is kind of long winded. To sum it all up: Spinning only for fishing jigs. Bait casting for everything else; surface, jerks, glides, twitch baits, bucktails, soft plastic swim baits, etc. If you can afford only one rig for casting for muskies, definitely get a decent quality bait casting outfit. $300, maybe a bit more will get you there.