For Cyph[1], we went with SPHINCS[2] for signing and a combination of McEliece (specifically McBits[3]), NTRU[4], and SIDH[5] for public key encryption.
We also considered QcBits[6] as a more space-efficient alternative to McEliece, but it just seemed too new / not well understood for our tastes, and last I saw there was a recent attack on it that hadn't been mitigated yet. Definitely keeping an eye on it for the future though.