HMACSHA1 vs HMACSHA2 (for PBKDF2) I need to choose an HMAC function for PBKDF2.

I'm using .net so I don't have the option to use SHA3. At first glance, and according to this answer by Thomas Pornin  it seems like SHA512 would be best.

However, I've heard that there are some possible downsides to SHA2 compared to SHA1. One of them possibly having something to do with quantum computers. (Yes, I know they're not practical yet, but why not choose better over worse?)

So the bottom line is - should I use HMACSHA1 or HMACSHA2 (512)? Or in other words, is the abovementioned answer a recommendation to always use SHA2 or is it dependant on some factors?

[Also, I would like to verify that I understand correctly that in any case, I should only ask it for the native output (160 bits for HMACSHA1 and 512 for HMACSHA2-512 - right?). Right?]

More (possibly relevant) info

I have a requirement to use only Microsoft libraries. And I need to implement a password stretching function with feedback - how far is the function done. So I can't use Rfc2898DeriveBytes (which doesn't provide feedback), nor SHA3 (unless I write it myself. But I've already written the PBKDF2 myself, and would rather use a built in HMAC rather than write that too.).
The only downside to SHA-2 over SHA-1 is that SHA-2 is a little slower.

In this case, that is of no practical consequence whatsoever because you're trying to make something slow to compute, and it is only a matter of raising the number of iterations to make it cost a certain number of bit operations in serial.

However, please consider using the modern memory-hard password hashes scrypt or argon2 instead of PBKDF2, to limit the advantage that attackers with highly parallel low-memory GPUs, FPGAs, or ASICs can attain over the defenders using ordinary CPUs.

Of the SHA-2 family, SHA-512 is a little faster than SHA-256 on CPUs with native 64-bit integer arithmetic, which are the vast majority of personal computing devices today.  So it provides a tiny advantage to the defender to use SHA-512 instead of SHA-256.