SQL 2012 :: Limiting Query Results With 3 Criteria For Each Record

I am trying to write a query that gives me the personal records from speed skaters on e.g. the 500 mtrs. I do this with the query:

SELECT cdsDistance AS Distance
, prsFirstName
, prsLastName
, min(crtFinalTime) AS MinTime
FROM tb....... INNER JOIN etc..
GROUP BY cdsDistance, prsFirstName, prsLastName
ORDER BY min(crtFinalTime)

In itself this works fine. However, there are complicating factors. Sometimes a speed skater has multiple PRs, meaning the he/she has the same fastest time more than once.

If these times are achieved on multple days, the 1st date is the official PR. (meaning: "Min of racedate")
If they are raced on the same day the 1st race is the PR (meaning: "Min of distancenumber")

Changing the code to:

SELECT cdsDistance AS Distance
, prsFirstName
, prsLastName
, MIN(crtFinalTime) AS MinTime
, MIN(cdsStartDate) AS RaceDate
, MIN(cdsDistanceNumber) AS DistanceNumber

FROM tb.......
GROUP BY cdsDistance, prsFirstName, prsLastName
ORDER BY min(crtFinalTime)

This gives me the wrong outcome because it gives me the "MIN" of every field, and they are not necessarily on the same row.

An option would be to calculate min(crtFinalTime), if for a person there is more than 1 result, calculate min of date, and then (if there is still more than 1 row) min of distancenumber.

Seems complicated, and I have the feeling there must be a better way (apart from: how to get this code)

Stacking subqueries in the FROM statement seems like a option be costly (time wise). There are more than 10 million rows (and growing) to run through.

As an example a few times:

DistanceFirst nameLast name Time Date Distance nr.
500 Yuya Oikawa 34.49 201311155
500 Yuya Oikawa 34.49 201311153
500 Yuya Oikawa 34.49 201311172

Yuya has 3 best times (34.49), 15-11-2013 is the 1st date, then distance nr 3 is the 1st distance raced. Therefore the 2nd row is the only row I would like to get in my endresult.