Personally, as public key cryptography goes, I think RSA should be used. There are multiple reasons for this:
RSA has been proved secure by many people
RSA is widely used and implemented, therefore info is widespread
RSA is theoretically quantum proof, provided you use a large enough key
RSA keys can be multiple sizes
You could use Elliptic curve ...
You just need to hash your password once with a secure algorithm
I will develop my statement using Elliptic Curves as they are as robust as RSA for smaller keys (256bits for EC and 3072bits for RSA give the same security), and faster to compute. Also, RSA key requirements differ as you need to find primes.
In Curve25519 paper you have this for private key ...