I'll probably repeat a few things, but had to add my 2 cents . . .
I second the idea of baking brie, which is much easier than it sounds and packs a nice wow factor. Just thaw frozen puff, wrap it around the brie, maybe brush with a beaten egg yolk and sprinkle with salt, and bake. Alternatively, you can bake brie right in the round wooden box it comes in. It is delicious to dip crusty chunks of bread into, and is a perfect way to make a less expensive brie better. You just take the top off of the box and cut a circle in the top of the brie, and you have a melted, yummy center. Be sure to steer clear of soft cheeses with stabalizers, which makes them terrible.
I also agree with talking to Mike the cheese guy at Curds & Whey. He can be very helpful and will help you make the perfect cheese plate. He has helped me on many occassions and is very nice and will find out what you are looking for, and will then match up your tastes. Or, if you don't have a particular taste, can assist you in making a well-rounded plate.
I might steer you away from Grapes in the Market, only because he tends to have only more expensive bottles, and you might reach your limit before you have enough wine. For the record, you can buy wines at retail prices from the Burgundy Room in the Short North, and they have a great selection of bottles in the $15-$20 range. I also like Spagio Cellars in Grandview; they have really knowledgeable sales people there who could help you pair things.
I would personally start with the cheeses and then pair the wines. And actually, whites usually pair better with cheeses than reds, particularly flavorful, fruity whites. If you are looking for an inexpensive madeira option, I am hugely fond of Jonesy, which is an Australian madeira-style wine which costs around $15 a bottle. I think you can get it at the Anderson's, which, by the way, is a GREAT place to buy wine. (Off of Sawmill road in Dublin).
I always like to have lots of nuts and dried fruits to go with cheese, and Trader Joe's is the perfect place to buy those sorts of things for less than anywhere else. Definitely buy some Marcona almonds at Trader Joe's - both the salted ones and the rosemary ones. YUM.
I love Carr's Tea biscuits with soft cheeses (or you can buy digestive biscuits at World Market); they are similar to a grainy graham cracker, and they are heaven with brie.
Oh, and I love the baguettes from Eleni Christina in the Short North. I'm not crazy about some of their breads, but the baguettes are great, especially for cheese.
And lastly, since you live right nearby, Katzinger's also has a great cheese selection, but I'm not sure how helpful the staff will be.
Good luck! I hope it's fun!!