Some R20 leves that are decent:
The Devilet Inside (Camp Horizon) [lalafell assassins/wisps/devilets]
The Wights' Stuff (Camp Horizon) [skeletons, this one is difficult, don't go high on stars]
Securing Horizon's Edge (Camp Horizon) [humanoids, this one is difficult, don't go high on stars]
Save the Lettuce, Save the World (Camp Bloodshore) [dodos, beware breath!]
Obviously start in Ul'dah and grab the Horizon leves and run out there and do 'em. Always make sure you kill the max amount of mobs on D.I leve. If you pop the Devilets, just run away and kill the rest of the assassins and wisps. You can really rack up SP on this one. After that you can head out Bloodshore, or just grind in Nanawa once you are high-20s. Save favor for the top three always. I would start DI on 2 star and the rest on 1 star until you are in the mid-20s. Then add a star to the leves every 3-4 average ranks in your party. Continue to do these in the loop on 4-5 star until the low-mid 30s while doing the Rank 30 leves to fill out the 8. Helps if you have everyone set a favorite in Horizon and Bloodshore to split Anima costs.
And as soon as you can pickup R30 leves, check these out. Start on 1-2 stars in low-mid 20s, then 3 stars until your whole group is ~33-35. Add a star every 2-3 average ranks in your group thereafter:
Necrologos: Adamantine Wills (Nanawa Mines) [you can start this one on 2-3 stars since the targets are Coblyns]
Necrologos: Levinshower (Nophica's Wells) [sheep targets]
Necrologos: Lightsome Verdure (Cedarwood) [gnats, be careful on star selection.]
Necrologos: Inferno (Cassiopeia Hollows) [slug targets, watch AoE]
Necrologos: The Moons' Mistress (Mun-Tuy Cellars)
What my group did was we all start grabbed Wills and Levinshower in Ul'dah, then headed to Mines to do the former, then ported to Horizon and hoofed it to Wells. Have 2-3 people set Horizon as a favorite camp to save Anima over time. After that we had someone take us to LL, we'd grab/refresh Lightsome and Inferno, run out to Cedarwood, do Lightsome, and run to CH and do Inferno. Save favor for these 4 leves always. You can get anywhere between 7-20k doing these depending on how (un)lucky you get doing them. We rarely bother with Moons' Mistress because it's just not worth porting out to Gridania, but if we did, we would just grind afterwards (we usually do regardless).
As people have already stated, in order to make sure you maximum leve-linking, you wanna get as many people in your party with these leves, so those people who have them should never trade them in, just refresh em at the guild counter ever reset. You will fail these leves (leave one mob up and run away, abandon the leve at the aetheryte, logout, or run out of the guildleve area). If you have 6 people with all these leves, it's best to do each leve twice with 2 links each and favor. That way you double up your leves essentially. It's great to have a huge party for leves. I mean imagine you had 15 people all with the same leve. You could do that leve 4 times with 3 x3 links and 1 x2 link. It will be great bang for your buck that way.