Which background is a better complementary for a strategy manager? Marketing, Finance, Sales or Supply chain?

I would consider that the answer is dependent on the company looking for a strategy manager.
Or reverting the comment, considering which complementary skills a strategy manager wants to acquire, targeting specific industries/companies.
All of these elements are important, there is probably no way to build a solid strategy without considering Finance, Sales, Marketing and Supply Chain (plus probably few other aspects such as HR, Innovation).
Now, individual companies put more emphasis on one or the other, this is also what differentiates them and builds their competitive advantage.
Just to reflect on the excellent research from Tracey and Wiersema (1997), what makes/made IBM, Apple and Dell? IBM focus was a unique approach to Sales, Apple was all about Innovation, Dell was all about their Supply Chain, giving each of them a unique winning value proposition.
Does not mean that they were not considering other elements, but their Strategy was highly guided by these specific elements.
To summarize, I would suggest that the better complementary background depends on the company you work for, or the company/companies you'd target.

Create Inventive Solutions

Finance ,while you work to develop a strategy it must be within the organisation's Financial framework

Marketing followed by Supply Chain and Sales

change your plan to perform mission .

The strategy is derived from Market Dynamics. All strategies are based on customer's voice. 

You start from customer's voice and go backward to finance and supply chain. Try to have customer centric organization.