This is the minefield. You may not lose an arm and a leg, but mediocre wines with famous names may cost that much. If in Bordeaux the great names produce fine or great wine on a consistent basis, Burgundy is a region where even money can’t buy you consistently fine or great wine.
We’re talking two colors here. Great white Burgundies are Chardonnay and are traditionally more reliable than the reds (although now many wines are aging prematurely). The great names of Meursault, Chassagne and Puligny are expensive, but rarely will any but the least expensive bottles fail to provide pleasure... at least if they don’t oxidize at a young age.
Red Burgundy is different. The grape is Pinot Noir, the world’s most fickle and finicky varietal. Thin-skinned and lacking in anthocyanins (colorants), low yields are a necessity to make good wine. A warm, sunny growing season is also mandatory. Unlike in Bordeaux, the famous names are of vineyards (Chambertin), not producers (Château Lafite).
Famous vineyards can have many owners as well as widely varying soil and terroir. Chambertin can come from a great grower in the heart of the vineyard. In the best years this will be a powerhouse of infinite glory. It can also come from a poor négociant buying from a careless grower with a fringe parcel, in a cold year. Yet it still bears the famous name and is labeled “Grand Cru” It is easy to pay 3 digits for something thin and nasty.
There is no inexpensive red Burgundy, but moderately priced ones can be good if grown, made, cellared, and bought with care. Wise counsel suggests finding growers, négociants, importers and/or stores you trust. There is no insulation from possible disappointment but this is the best that anybody can do.