Before the Romans, Celts and Greeks were my favourite two factions, now all three share a top spot, and though i've got all of them well geared, I play this game quite casually but can still do most legendary quests... eventually. Hopefully, that means I can offer suitable advice.
Celts
Celts have several core strategies they can use, depending on circumstances.
Their spearmen are "cheap" in that they only cost food, and Celts get good farm upgrades meaning you can essentially get 20-25 farms, 10 barracks, and print an unending tide of spearmen to block the enemy and grind them down. Celtic spearmen also get bonuses against buildings, and with overwhelming numbers they can chew through a base slowly and surely. You can mix in a light sprinkling of druids too, to buff damage and add AoE healing, and this is also a good time to use more or less any of the animal sacrifice buffs.
Another strategy: use longswordsmen like legionaries. You will need a market and a few trade caravans as well as farms to support spamming them, of course. druid support is good, and carpentoms with their champion upgrade add a little bit of splash damage from the rear lines. I wouldn't reccommend too many though as i don't find them to hold their own very well for a unit that costs 3 population.
As mentioned above, another good unit to mass is the Champion. Not specialised against any unit means high damage and decent enough against everything, and also they do have that most lovely of things, splash damage. the bigger the fight the better they do. They're not as big, expensive or powerful as elephants or berserkers but they get the job done well enough. Using King brennos as your age 4 advisor is... advisable.
Greeks
I'm a simple man. Endless swarms of tanky hoplites with 4-8 ballistae sheltering behind them to target down larger groups of enemies or deal with buildings is my preferred strategy. Sometimes I use the heleopolis advisor because i like AoE pierce damage (also mixing ballistae and heleopolis means 2 different fire rates, and 2 different damage types. less wasted damage in overkill, and pierce/crush damage compliment each other nicely). Having your ballistae/heleopolis grouped with some (maybe 20) of your hoplites and putting them on hold ground, moving them forwards bit by bit to support your front line is a good strategy, i find.
If you're finding your hoplites are countered and are dying too fast, you can switch them out for Hippikons, which are better general damage dealers, slightly less tanky per population, i find, but have a larger health pool and so live longer in the face of huge amounts of AoE damage.
Another variant on the ranged death ball involves either all Gastraphetes, or a mix of everything from the archery range, since having 60 gastra shots fired at one enemy is... a bit overkill for even elite enemies.
I understand where you're coming from with wanting to use only a single type of unit, each of the melee units i've mentioned works well enough on its own, the ranged parts just make it a lot stronger, and hopefully that's close enough to what you asked to be helpful.
TL,DR
The real trick is a strong economy and full blacksmith upgrades. With enough farms and caravans, you can afford endless infantry and cavalry, and so long as you have about 10 barracks/stables less than 2 screens away from where the fight is happening, you can just overwhelm your enemy with numbers, regardless of wether it's spearmen, longswordsmen, champions, hoplites or hippikons. Siege/ranged support is optional but very helpful if you've reached heavy fortifications.
