The Telecaster on Led Zep 1 is correct. Interesting because people always associate him with a Les Paul. The guitar does sound like a Les Paul on that album.
I have heard that they were Plants kids, but I've also heard that's an 'untrue' rumor. Hard to know what to believe.
I had read that the amp Clapton used for that track was a Pignose amp (little batter powered guy). Clapton walked into the studio & put it on a folding chair as his setup. Some of these 'rock and roll facts' are a little hard to verify.