How much would it cost to go from 20-52 summoning?

Including shards/ pouches....

 

Also: what is the most efficient way?

Depending on this, would it be worth my time to get the secondary "ingridient"

myself, or just buy it?

Since your sig states you're more of a.. skiller initiate pure, you shouldnt have trouble making money(?).

Basically the best things to do are use your lower level ones, mostly greens until Honey Badgers. Use most, if not all your crimsons on those.

 

The real question is though, do you want to get higher summoning than 52, or just keep it there?

Do penguins and tears of guthix for lower lvls. It's a waste of charms otherwise IMO.

Its only a waste if he/she plans on getting higher levels - if not, then he/she should just get 52 with all the charms.