I'm amplifying a transgene using Pfu and plan to double-digest it with NotI and XhoI (same buffer) to ligate it into a plasmid. I've never done high-fidelity PCR and I'm not sure what the primers should be dissolved in (i.e., water, TE, or just Tris; pH=8?). I'm also uncertain if the cellular debris in the lysate should be removed before PCR (phenol:chloroform with 2-3 chloroform washes?).