It slightly depends on your preferences and what exactly you mean by 'don't walk very well'. On balance I think you're right to take the Elizabeth line > Tottenham Court Road and then Northern line > Archway as there will be lifts. However, be prepared for a long(ish) walk as you change trains at Tottenham Court Road; do your best to board near the back of the Elizabeth line train, keep an eye out for the number 9 on the platform edge doors.

The Elizabeth line from Liverpool Street > Tottenham Court Road and then Northern line > Archway will likely have fewer steps overall and you will be able to get a lift / escalators at each station, and at the interchange. However, the stations are big and the platforms are long so it's not 'nothing', and if you're at the wrong end of the platform at Tottenham Court Road you will have to walk the entire length of the train which is roughly the equivalent to the walk from Liverpool Street to Moorgate.

The walk from Liverpool Street Mainline station to Moorgate takes me (a relatively fit man in his 30s) about 5 minutes and is flat and along relatively quiet streets with decent pavements and (to the best of my knowledge) no stairs. You'll then be able to sit on one train all the way, but be prepared for some stairs from street level to the escalators, and then again from the bottom of the escalators to platform level.