For SQL Server, there are many factors that contribute to the final execution plan. On a basic level, Statistics play a very large role but they are based on the data but not always all of the data. Statistics are also not always up to date. When creating or rebuilding an Index, the statistics should be based on a FULL / 100% sample of the data. However, the sample rate for automatic statistics refreshing is much lower than 100% so it is possible to sample a range that is in fact not representative of much of the data. Estimated number of rows for the operation also plays a role which can be based on the number of rows in the table or the statistics on a filtered operation. So out-of-date (or incomplete) Statistics can lead the optimizer to choose a less-than-optimal plan just as a few rows in a table can cause it to ignore indexes entirely (which can be more efficient).
As mentioned in another answer, the more unique (i.e. Selective) the data is the more useful the index will be. But keep in mind that the only guaranteed column to have statistics is the leading (or "left-most" or "first") column of the Index. SQL Server can, and does, collect statistics for other columns, even some not in any Indexes, but only if AutoCreateStatistics DB option is set (and it is by default).
Also, the existence of Foreign Keys can help the optimizer when those fields are in a query.
But one area not considered in the question is that of the Query itself. A query, slightly changed but still returning the same results, can have a radically different Execution Plan. It is also possible to invalidate the use of an Index by using:
LIKE '%' + field
or wrapping the field in a function, such as:
WHERE DATEADD(DAY, -1, field) < GETDATE()
Now, keep in mind that read operations are (ideally) faster with Indexes but DML operations (INSERT, UPDATE, and DELETE) are slower (taking more CPU and Disk I/O) as the Indexes need to be maintained.
Lastly, the "estimated" CPU, etc. values for cost are not always to be relied upon. A better test is to do:
SET STATISTICS IO ON
run query
SET STATISTICS IO OFF
and focus on "logical reads". If you reduce Logical Reads then you should be improving performance.
You will, in the end, need a set of data that comes somewhat close to what you have in Production in order to performance tune with regards to both Indexes and the Queries themselves.