In reply to nickh1964:
Assuming you’re going to be camping, you don’t need to book anything. Most treks are short, out of one valley and into the next, 2-3 days. The ones in the Lake District tend to follow trails through thick forest below the snow line, and need no special equipment (other than the best waterproofs that money can buy!!). Torres del Paine circuit is longer but mostly low level.
Recommendations: all of them! Every single one we did was brilliant. We used the lonely planet trekking in Patagonia book, effectively pre internet days (2000) buy found that entirely sufficient
did termas de Callao (chile, near lago todos los Santos), paso de las Nubes (Argentina, near bariloche), coastal trek on chiloe. Abandoned attempt on the dientes circuit on Isla navarino due to heavy snow. Did the Paine circuit- phenomenal.
We used a 3 season tent (terra nova solar 2) and found it to be ideal. MSR dragonfly stove- fuel widely available. We tracked down some Chilean IGM maps in Santiago, but needn’t have bothered- you’re either on the trail, or you’re thrashing about in bamboo thickets and the map is completely useless either way.
Chile and Argentina both very friendly places, with decent infrastructure so getting around is straightforward. Some Spanish essential but easy to pick up.
It was one of the best experiences of my life- hope you have a great time!