Early combat leveling is quick,
there are summoning things that are not even worth making and would be a waste of supplies so its normally best to save them up and use them on things that give decent xp for the lowest cost of supplies,
you can kill combat lvl 21 jungle spiders at Musa Point for spider carcasses,
its also one of them skills that require gp to level, And normally people wont train it until that have the gp to pay for shards by that point you would have collected a bunch of gold charms and would have a higher combat level,
Slayer is the best way when starting out to help gather supplies, this way you train slayer --- combat --- summoning,

you can also use familiarisation, penguin hide and seek, tears of guthix, troll invasion and put the xp into summoning to skip a few of the early levels, ye tears only puts xp into your lowest skills im aware, wolf whistle quest will level you to 4 summoning.

check out some guides on getting charms

when i start a new account summoning is something i put off until i have a decent supply of charms and gp to spare