I'm going to try to rulify my suggestions, so they can be poked at.
Rituals
The first important thing is that Rituals are divided into categories, or given relevant keywords, so that they are accessible according to your skill training. Most relevant to what I am writing here is that there will be healing rituals, suggested as follows:
Cure Light Wounds (requires training in Heal)
This ritual takes 5 minutes to complete and requires 10gp worth of medicinal components such as herbs, salves, gauze and thread. It restores a number of hitpoints equal to the Wisdom modifier + Heal check bonus of the person perfoming the ritual to a single patient, who may be themselves. A patient healed by this ritual cannot regain any more hitpoints from another Cure Wounds ritual until they are again significantly injured.*
Cure Moderate Wounds (requires training in Heal)
This ritual takes 5 minutes to complete and requires 50gp worth of magical and medicinal components such as herbs, salves, blessed gauze and thread. It restores a number of hitpoints equal to 10 + the Wisdom modifier + Heal check bonus of the person perfoming the ritual to a single patient, who may be themselves. A patient healed by this ritual cannot regain any more hitpoints from another Cure Wounds ritual until they are again significantly injured.*
Cure Serious Wounds (requires training in Heal)
This ritual takes 5 minutes to complete and requires 250gp worth of magical components such as rare herbs, blessed salves and holy water. It restores a number of hitpoints equal to 25 + the Wisdom modifier + Heal check bonus of the person perfoming the ritual to a single patient, who may be themselves. A patient healed by this ritual cannot regain any more hitpoints from another Cure Wounds ritual until they are again significantly injured.*
The costs and amounts restored are very hard to judge at the moment, but you get the idea. *denotes that you shouldn't play silly buggers and deal 1HP damage to someone just to cure them some more - I tried to avoid a direct GP-to-HP conversion, so that cheap rituals are more efficient, and the advantage of the higher rituals is time-saving. Parties will naturally start with Light rituals, but as they gain HP and start taking bigger hits, they should value more effective, if expensive, healing. I've also considered the cost of a potion, 25gp, which is the other healing option. Potions should generally be more expensive, since they are available in combat.Speaking of which, crafting such potions should be a ritual, not a feat.
By default there will be no Cleric spells that restore HP, though I would favour a cantrip that prevents bleeding at a distance, for downed allies. A Cleric of the Lifegiver, however, would channel divinity, or have a domain feature, or domain spells that do heal. My preference would be the use of channel divinity, restoring HP at around the same values as level-appropriate potions - in effect this Cleric saves the party actions and gold by becoming a walking potion-fountain. I would offer all Clerics the option to pick Heal as a trained skill over a Knowledge, so that in theory any Cleric can still fulfil the healer role.