You won't really be able to piece anything together for under $200. At anything below about $400 really you're much better off just buying a boxed set.
You may be able to snag good deals here and there on individual clubs, but really anything you can buy individually in a store is going to run you at least $60 a club, and often times more than that for something more decent that you'd be able to get in a set anyway.
Are the Dunlop you have now Cavity-back? Cavity-back clubs won't give you as much distance, but they're much easier to hit because they have a much bigger sweet spot due to the nature of the design.
What sporting goods stores do you have in your area?
If all you have is an Academy, then the Wilson Ultra club set should come in close to your price, and they're probably the nicest set of clubs they have in that price range, unless your store carries different stock than those around here.
If you have a D1ck's or a Golf Galaxy, then I'd recommend saving up an extra $100 and taking a look at the Maxfli Black Max set. My friend got a set of those and I've hit them a few times and they're quite nice for the money. I was in D1ck's a couple weeks ago picking up my new 52 degree wedge and I saw they were clearancing those out for $299 for last year's model, I don't think you'll be able to beat those at that price. The low irons are hybrids, which is nice because they're easier to hit.
Club fitting and all that is good to do eventually, but if you're just starting off your swing shape and speed are going to change as you get better, and IMO club fitting up front in your situation doesn't make much sense, not to mention that if you're even talking about club fitting you're looking at more expensive clubs.
Welcome to the wonderful world of golf, it's highly addictive if you enjoy it.