Angostura aromatic bitters remain the benchmark for a classic Manhattan for good reason, but you certainly do not need to spend a lot of money to explore some wonderful variations that elevate the drink.
First, I would highly recommend picking up a bottle of orange bitters, such as Regans Orange Bitters No. 6 or Angostura Orange. They are widely available, cost about the same as standard Angostura, and last for hundreds of drinks. The classic bartending technique is to use a split dash, meaning one dash of standard aromatic bitters and one dash of orange bitters. The citrus oils brighten up the heavier notes of sweet vermouth and whiskey without masking the spirit.
Peychaud's bitters are another affordable, versatile staple usually found in standard grocery stores. While traditionally used in a Sazerac, their lighter, floral, and subtle anise profile works nicely if you find standard Angostura slightly too heavy or clove-forward.
If you want to venture slightly further into flavor variations while staying budget-friendly, Fee Brothers Black Walnut bitters or Aztec Chocolate bitters are reasonably priced and pair exceptionally well with the oak and caramel notes of standard bourbon and rye. A single dash of walnut bitters alongside your Angostura adds a wonderful warm, nutty depth for cold evenings.
For practical everyday use, keeping just two bottles on hand—standard Angostura aromatic and a reliable orange bitter—will give you everything you need to make both standard and split-bitter Manhattans of exceptional quality.