The closest to my choice is: C. (a) 2048; (b): 4096; (c): I would not use RSA
My answer takes in account not only details mentioned in question, but currently widely deployed security practices. I try to point out useful resources to study.
Things are not as simple as pick one of A-D. I recommend to study resources I've included and draw your own conclusions.
US government has recommendations for security levels used in asymmetric cryptography. The systems used by US government agencies are validated according to these recommendations and only approved systems are allowed to be used.
Even if you do not intent the application for use by the US government, it is a good idea to at least meet (and occasionally exceed) their recommendations.
The modules lengths for RSA are defined in document FIPS 186-4 (Digital Signature Standard, version 4). The document defines these three levels:
- 1024 bit modulus (approx. equivalent in strength to 80 bit symmetric key cryptography)
- 2048 bit modulus (approx. equivalent in strength to 112 bit symmetric key cryptography)
- 3072 bit modulus (approx. equivalent in strength to 128 bit symmetric key cryptography)
The lowest of these levels (1024 bit modulus) has been deprecated. US government agencies are no longer allowed to use 1024 bit RSA, except for certain legacy uses. (For more detail read NIST SP 800-131A.)
In interest of interoperability, it is not recommended to go below 2048 bit modulus (minimum for US government, and actually, some other organizations as well) even if assumed attackers have only single computer.
If the attacker has large number of PCs (for instance all computers in internet), 2048-bit RSA should resist attack for quite long time (maybe indefinitely). 768 bit modulus is largest that has been publicly broken, and it is expected that governments may be able to break 1024-bit RSA modulus. However, in interest of stronger security and preparing for future, I recommend stronger (such as 3072 bit) modulus against attackers, who have large computational capabilities.
The part of question quantum computer is unclear. Assuming it means device which can run Shor's algorithm, then you may want to refer this question: RSA key length vs. Shor's algorithm. Then again, it is possible to purchase a quantum computer. But the ones available for purchase (such as D-Wave) are not useful in breaking RSA.