for a war cleric I considered Magic initiate for melee cantrips (and maybe a familiar)?
Magic Initiate (Wizard) is a great choice for a melee cleric, to get BB/GFB and another utility cantrip of your choice, plus 1/day Find Familiar or Absorb Elements.
One big issue in any case is bonus actions with extra attacks from war cleric competing with spiritual weapon and melee cantrips meaning no "attack action."
Yep. This is why a different type of Cleric with access to a melee cantrip is often a better option for a melee cleric than a War Cleric. Clerics have better things to do with their bonus actions than taking a measly 3-5 extra attacks per day. War's infrequent +10 to hit isn't all that useful either.
Arcana isn't the best option either. Yes, it's an easy way to get you one or both melee cantrips at 1st level, but there are other ways to do that, and none of Arcana's other abilities or domain spells (with the exception of Magic Weapon) help you out in melee. They don't even get Heavy Armor or Martial Weapons, although I suppose you could get by in a pinch with a 14 DEX and medium armor, plus some racial martial weapon proficiencies from being a Dwarf or Elf. Still not ideal, though.
When deciding on a subclass for a melee cleric, you'll want to start by looking for Cleric subclasses with Divine Strike at 8th level to add damage to melee, not ones that get Potent Spellcasting to add damage to cantrips. Subclasses with Divine Strike are Death, Forge, Life, Nature, Tempest, Trickery, and War. (Of these, Trickery is easily the weakest, since it adds Poison damage, to which enemies are commonly resistant/immune.) Then narrow it down from there to subclasses that have other abilities that are further beneficial to a melee fighter.
Forge has a number of great abilities and domain spells that help boost your defensive and melee capabilities. The only real downside to Forge on a melee cleric is that they don't get any Martial weapon proficiencies. However, that can be partly mitigated with racial weapon proficiencies from something like Elf or Dwarf, and/or by using your Blessing of the Forge ability to give your weapon +1 to damage. The difference in average damage between some Simple and Martial weapons, especially one-handed weapons, is typically only 1 point anyway. For example, a Mace, Handaxe, or one-handed Spear doing 1d6+1 damage with Blessing of the Forge has the same average damage as a one-handed Warhammer, Battleaxe, or Longsword's 1d8 damage. But that does mean no Greatsword/Greataxe/etc... (Though you'll probably be wanting a one handed weapon and a shield on a melee cleric anyway, even if you do have Martial weapon proficiency.)
Tempest is also a good choice, with not only good armor/weapon selection and Divine Strike, but also a nifty reaction ability to damage melee attackers. It also allows you to mix it up with some effective AOE on top of your melee ability, making you better than a straight melee combatant against masses of weaker enemies. (I think Tempest makes some of the very best melee clerics, but I understand wanting to try something different, having already played a Tempest Cleric recently.)
A Nature Cleric can also be solid, with both Heavy Armor and access to Shillelagh so club/quarterstaff attacks are magical, do d8 damage like Martial one-handed weapons, and key off WIS. This means you don't have worry much about DEX or STR and can focus on CON/WIS instead. You can even cast Shillelagh plus a melee cantrip together in the same round, so it's not like you have to spend a round getting your melee attack ready. Plus they get a wide selection of elemental damage types to add to your melee strikes at 8th level, allowing you to tailor your bonus damage around the enemies' resistances/vulnerabilities. (The downside is that Nature's domain spells aren't very useful, at least for melee.)
No matter what, you'll want to take Warcaster at 4th level, to allow you to use your melee cantrip on Opportunity Attacks, boost your Concentration saves, and cast while wielding both a shield and weapon.
As for races, a Variant Human could take Magic Initiate right off the bat, or take War Caster at 1st and then Magic Initiate at 4th.
Hill Dwarf is a solid choice for a melee cleric, with bonuses to CON and WIS, extra HP each level, and no decrease in speed when wearing heavy armor so you don't necessarily need a high STR. It also gets proficiency in Martial hammers and axes, which helps on a Forge cleric. But you'll still be having to spend a feat on Magic Initiate, which means delaying taking War Caster and your ASIs by 4 levels.
For something a little different, you could also try a High Elf, taking BB/GFB as your racial cantrip, so you wouldn't be reliant on spending a feat to get access to a melee cantrip. You'd also get proficiency in some Martial swords and bows, if you don't get that from your subclass. DEX and INT bonuses usually aren't very helpful for a melee cleric, but this opens up the ability to go for a DEX-based High Elf Cleric, with Light or Medium armor and a Finesse weapon. Forge wouldn't be quite as optimal for that route, since a couple of their abilities center around wearing Heavy Armor, but it still has some other good stuff going for it even for a Light/Medium armor character. And some of the other subclasses would excel as a DEX-based Cleric.
(Come to think of it, a Dex-based High Elf Tempest Cleric with Booming Blade and a Rapier seems like a nifty and thematically-consistent basis for a character. Or take Spell Sniper and use Booming Blade at 10 feet with a finessed Whip for extra style!)
