Next to Moon Druid, the most capable Druid Circle for Melee is Spore Druid. The Halo of Spores and Symbiotic Entity Features are pretty darn “gishy” already… temporary HP, 1d6 poison on melee weapon attacks plus additional damage using your reaction.
That being said, here a few idea for building a Spore Druid Gish.
Avoid the temptation of dipping into martial classes like fighter, monk, or barbarian. At low levels this may be OK but you are really going to be cutting into your spell progression and overall power for a few modest martial gains. Monk and Barbarian are OK for Moon Druids but I wouldn’t pair those classes with Spore Druid. If you multiclass, do so with another full caster class like Cleric.
Avoid builds that rely on using your bonus action for an extra attack. Again, this is going to be very tempting as more attacks equals more poison damage. I’m thinking about the Polearm Master Feat or the Monk’s Flurry of Blows. Again, assuming a Spore Druid Build, your bonus action would be better spent ramming a Flaming Sphere into bad guys and/or mentally commanding your Undead thralls to attack.
Your build should include Booming Blade and Green Flame blade. The SCAG cantrips stack with Shillelagh and Symbiotic Entity. You still only have 1 attack but it will be a big hit. Green Flame Blade will also allow you to target 2 opponents w/n 5’ of each other
With all that in mind, here are my ideas:
Race: Tortle/Lizard Folk/Loxodon. All these races give you +1 Wisdom and natural armor which stacks with a shield. You could easily start at Level 1 with 17-19 AC
Build #1: Spore Druid X/Arcana Cleric 1. A dip into Arcana Cleric will net you Booming Blade and Green Flame Blade and access to 1st level cleric spells like Inflict Wounds and Guiding Bolt. Shield of Faith or Protection from Good and Evil can also help you “get in there and gish”.
Race: Hill Dwarf
Build #2: Spore Druid X/1 UA Stone Sorcerer. The build will require an investment of 13 CHA but will net a several benefits including proficiency in CON saves (if you start sorcerer), Stone’s Durability, the SCAG cantrips, Shield Spell plus 1 Smite Spell. Like the build above, you will get a very high AC from Stone’s Durability and Booming Blade and Green Flame Blade to stack with Shillelagh. The smite spells Thunderous Smite or (my favorite) Wrathful Smite ALSO stack with Booming Blade, Green Flame Blade and Shillelagh. That will be a lot of damage dice to roll. Downside of this combo: it uses your action and bonus action and concertation.