I fish wacky worms a lot. I've fished them on $50 to $150 baitcasters, 2pc ugly stick baitcaster rod to $100 one piece St. Croix mojo rods. I've used 12lb mono, 12lb flouro (multiple brands), 30lb braid, 50lb braid, (power pro reg and super slick). In fact I just made a post about a good evening with them in fishing reports! http://www.bassresource.com/bass-fishing-forums/topic/120570-fun-evening-with-wacky-worms/ .
In my opinion you can do it no problem with your $200 budget or even a goal of $150, but imo $200 is a better place. This is a combo I used just recently and it's right in your $200 budget.
Lew's Tournament MG ($105~ online, $130 retail)
Mojo bass rod ($100~)
or
Shimano Clarus worm & jig rod ($80~)
Then pick your favorite line, I like fluoro for wacky worms. However, I fish in areas with tons of weeds and tons of lily pads, so I use braid for now, 30# on one rig and 50# on another. I also like the braid for the no stretch and sensitivity and find it better around lily pads. 30# is probably lowest you want to go because the diameter is small it can dig in. The 30# I have is regular power pro and the 50# is super slick, very noticeable difference in smoothness, noise and casting performance.
For reference, my fiance is using the Shimano Clarus 2pc worm & jig rod with a Quantum escalade HD baitcaster, 30# power pro braid, she fishes wacky worms I'd say 90% of the time, so even with the cheaper and older reel, it's np. I use my mojo bass 'plastic' with my tournament MG and 50# power pro super slick braid and I can toss them pretty far.
I can try to take a video to show you casting distance between the rods & reels I have when I get time. But do not worry you can easily fish wacky worms with baitcasters. I typcially use the the $3 strike king packs (shim-e-stick) and the $3 yum packs you can find at walmart. (dingers)