Three members of our party want to leave but one of them is a cleric who is our healer. Since we are levelling up to level 4 we could take on feats and there is the feat of Healer or of Magic Initiate, the latter allowing us to learn a first level healing spell.
What would be the best option or are there any other options to replace our healer?
Since there are no healing cantrips and none of the first circle healing spells are worth taking as the only healing if they can only be used once a long rest (aside from goodberry but if your party is that desperate for healing I would suggest that your DM might be using too difficult encounters), I would recommend against taking the Magic Initiate feat for healing.
The Healer Feat is pretty nice since it essentially turns the healer's kit into ten potions of healing (not exactly, but the differences are mainly nitpicking).
Alternatively if your DM is using the 5e rules for resting as long as you stay cautious you won't need any healing aside from what you get resting and from items. However, that last option is particularly risky and can lead to a party wipe.
Hopefully this helps!
There are optional rules in the DMG about pricing and buying magic items. If your DM finds it suitable, it's theoretically possible to get Potions of Healing at 50-100gp. It's not recommended that your shops have an unlimited supply, but it's pretty reasonable to provide enough to make up for the most basic healing spells.
It is quite unrealistic that your party finds hundreds of Potions of Healing during adventureing. Even if they could, it is a huge waste of resources.
Healer: It was mentioned before, quite an obvious choice.
Inspiring Leader: Does not give you as much HP as Healer, but in many ways it is still better. If your Fighter with 30 HPs receives a blow with 32 damage, this one keeps him swinging, so contributing to the victory of the team. Healer only works the persont taking the feat is around, and can spare an action.
Magic Initiate: As name moniker said, one 1st level spell is not worth taking, and there are no healing cantrips.
Depending on your party composition, different options are the best. You can use any spell slot to cast a spell known from either of your classes. So a 3rd level Wizard/1st level Cleric can cast Healing Word in a 2nd level slot.
However, you should not forget the attribute requirements for multiclassing, both into and out of a class.
Bard: Often overlooked as healer, but it has better healing options than a Paladin.
Cleric: Great choice for a Wizard or Wild Sorcerer, best healing spells, Medium Armor (Life, Nature, Tempest and War even gives Heavy Armor).
Druid: As above, but the armor proficiencies are much worse. Two levels of Moon Druid can add a multitude of Wild Shapes, great for HP replacement. Especially good on a Monk, as they can use Unarmed Strikes while Wild Shaped.
Paladin: Surprisingly bad at healing, cannot cast spells until level 2, and does not gain Healing Word. Aura of Vitality is great, but you have to wait 9 levels for that.
If you have time and money, you can make your own potions of healing.
Someone with a herbalism kit and the proficiency to use it can craft potions of antitoxin and healing.
PHB, Chapter 8, Between Adventures, Downtime:
For every day of downtime you spend crafting, you can craft one or more items with a total market value not exceeding 5 gp, and you must expend raw materials worth half the total market value. If something you want to craft has a market value greater than 5 gp, you make progress every day in 5-gp increments until you reach the market value of the item.
So, a potion of healing (50 gp) will take 10 days and 25 gp of materials to craft.
While the PHB does specify that downtime crafting is only for creating nonmagical items (which a potion of healing is not), XGtE does call out a potion of healing as an exception. XGtE also drastically reduces the time required to 1 day.
XGtE, Chapter 2, Downtime Revisited, Crafting Magic Items:
Potions of healing and spell scrolls are exceptions to the following rules. For more information, see “Brewing Potions of Healing” later in this section and the “Scribing a Spell Scroll” section, below.
D&D is a game of choices, you always have to carefully weigh up the cost of choices.
Spending a feat uses up a valuable ASI. Choosing a multiclass uses an entire level. Even spending 50 gold is 50 gold you can't spend on something else, plus it takes up room in your backpack and weight on your back.
We often feel that we absolutely need a healer and healing, but "we need healing" isn't a problem, that's actually a solution. Your problem is that you want to fight more, win more fights, or more loosely, achieve more. Is this the best use of your resources in order to handle your problem?
Instead of spending significant resources to get a small amount of healing, consider if it is instead better to maximize your advantages.
A party is taking some damage in fights. A glass cannon wizard is considering multiclassing as a cleric to gain some healing options. Instead, they could get another level of wizard allowing them to deal more damage, expend more spell slots, and even pick up a control spell, that would allow them to kill enemies faster and reduce the amount of damage the party takes.
It is likely that any other choice will be more effective than options that being a level 1 cleric offers.
Generally speaking I think that levels, feats, and items magnify the effectiveness of a character, so making choices that work well with the character will be far more effective than trying to split your role.
Healing isn't all that powerful in 5e in the first place. A 4th level life cleric's channel divinity heals 20 hp (between 1 and 2 attacks from a CR 4 creature), their prayer of healing is 4 + 2d8 + modifier (again, between 1 and 2 attacks which they can do 3 times), cure wounds is 4 + 1d8 + modifier (between half an attack and 1 attack, 4 times). Even a 4th level cleric is not super useful - and I doubt anyone would want to completely reroll. There are better ways to use your resources.
Now, there are some obvious options: deal more damage to kill enemies faster so they can't hurt you, use control spells to prevent enemies from dealing damage, etc. However, fights are not so 1-dimensional.
Talk instead of fighting A fight avoided is a fight won. If you have a character that is good at social interactions, then they should work to maximize that effect. Other characters can even help them with spells or feats. Remember that if you skip a fight, then you have a whole fight's worth of resources (spell slots, per-rest features, and HP) that you can afford to spend on the social interaction instead.
Make sure fights are favorable Better scouting and positioning can be hugely beneficial. There is a big difference between attacking an orc raiding party when they are on the war path, and attacking them while they are cooking dinner and getting ready for bed. Try to maximize your party's ability to take fights on their own terms rather than using HP to account for unfavorable conditions.
Use your time more efficiently Consider the value of rests. Often we think of rests as being something we can't control - no matter the party composition you get X short rests and 1 long rest per 24 hours and you have to get the same amount of work done no matter what, but that isn't true. Your party controls what it does, that means they could take a lot of short rests, and take less fights per day to make up for the lack of healing. This means you have a lot more down time which can be spent for downtime activities, waiting for the rogue to scout, and social interactions. If your party already has ways to capitalize on downtime, consider taking more short rests per days and taking less combat per 24/hours.
While there are few ways to solve the problem of "we need more healing", there are tons of ways to solve the problem of "we want to accomplish more".
What would be the best option or are there any other options to replace our healer?
If your party is set on having a combat healer then multiclassing is the best/only way to go. The Healer feat is really only effective as an outside of combat resource since it is only usable once per character before a short rest. Consider how most fights go, is it (A) one person takes a majority of the damage and the healer casts spells every round to keep them standing or (B) everyone has some way to prevent or mitigate damage and you heal up between fights. If your group is doing mostly (A) and little to no (B) then you NEED the combat healer and the feat will not help. If your group is doing mostly (B) and and little to no (A) then the feat will be great for you. If you do some of (A) and some of (B) then you need a secondary healer for emergencies and the feat will take some of the load off the healer.
As for the Magic Initiate Feat, you could get a 1st level cure spell once between long rests, it is completely and wholly inadequate. Other choices involving stocking up on potions or other items. If you think about it, it comes down to class features, spells, feats, and items. Your parties classes control your access to spells. Feats really only provide out of combat support for healing. Items are too variable on acquiring them, that is to say maybe you can and maybe you can't get them.
TLDR: if your party NEEDS a healer then your best option is to get a healer. Don't short change yourself or your party with just a healing feat.
