Unfortunately, there's not really a reel out there in that price range that I'd feel very comfortable recommending, unless you happen to find a good used Penn 706 on fleabay or something, even those are usually going to go for a bit more. With reels, like many other things in life, you get what you pay for. In the long run you'll spend less money getting a quality reel to start with than getting a cheap reel that will only last you a season or two.
Since you say that you're wanting to fish both cut bait and plugs, I'd recommend the Shimano Baitrunner reel. They have a great reputation and will pull double duty (bait/plug) just fine.
Pair it up with a 9 to 11 foot rod from Tica, Tsunami, or step up just a bit to the Lamiglas Surf King and you'll have a pretty decent combo.
Just make sure that whatever rod you choose is rated for the weight range you intend to use it for. Keep in mind that most rods which are heavy enough to throw bait well are not going to do so hot with a 1 to 2 ounce lure, and a rod which is light enough to throw small lures well is not going to be able to handle a big chunk of lead and half a bunker. Most folks who fish both bait and lures will eventually get a rod suited for each purpose. I have yet to find a rod that excels at both.
Just my 2 pennies. Your mileage may vary