When it comes to expressing the idea of having successfully purchased something, there are several alternative terms to use other than "manage to buy." For example, one may say "secure" or "acquire" to suggest that the item in question was not easily obtained. Similarly, "obtain" or "procure" can be used to imply that some level of effort or skill was required to make the purchase. "Purchase" or "buy" themselves are also perfectly acceptable alternatives, but may lack the nuance of indicating a particular level of challenge or accomplishment. No matter which synonym is chosen, what's important is that the meaning is clear and precise.