Best units?

It all depends on how many souls you are prepared to shell out for each category. All have good cheap options, but the most expensive ones are mostly the best in stats.

Melee infantry has the Royal Swordsmen for the cheap option, but if you are an older player, you are likely to have gotten rid of your Two-Handed Swordsmen fragments. Up in cost are Blue Vikings (Nordic Heavy Axemen). They are diet Varangians (and don't have Bloodlust, which is great). Varangians are likely older players' go to, as they are cheap and are available in the gold shop occasionally. Hengdao is good but is also very expensive and unlocked relatively later. But because of that, many players don't consider them to be the best overall and opt for Varangians. If you don't spend, Blue Vikings/Varangians and Royal Swordsmen (if you haven't disposed of your Two-Handed Swordsmen) are the best in my F2P view.

For defense infantry, it doesn't matter too much. Phalanx are cheap and are unlocked very early. Lombards are a step up and are a nice unit to invest in if you find Phalanxes to be too squishy. Swiss Halbardiers have only recently been unlocked, but are a direct step up from Lombards, while Modao is just defense Hengdao. Lombards are a good choice here in my view, but Phalanxes can do early on.

For melee cavalry, Camels are cheap and work very well, while the Sipahis look good (someone will have to give me some more insight on their uses), but Teutons seem to be the best. Sepulchres and Black Armored Guards (not as mainstream as Jet Black I believe) are used for movement shenanigans. Camels are unlocked right at the early game, while Teutons (and to a lesser extent Sepulches) are expensive but are at the Crusades, and I would assume the Sipahis are at the new Ottoman campaign. Camels might be worthwhile, but Teutons are much better. It depends on how much you want to use melee cavalry, but since cavalry is too squishy, investing too much might be a mistake. Teutons are also more obtainable with Barbarossa for F2P. It depends on your need for a stronger melee cavalry, your willingness to get Barbarossa, and how much you are willing to spend on Teutons.

For charge cavalry, I would say Templars still rule, but Gendarmes are very good for debuffing, while Jet Black is also great for movement shenanigans. Ideally, one would have all three in a legion, but since even one unit would bankrupt you, Cataphracts are a great choice. They are just a F2P-friendly Templar, and are perfectly suited for their role. If you are F2P, get Cataphracts, if not, the first three units or just Templars (strong maybe on getting Gendarmes instead) will be better.

Ranged infantry isn't too good, but Ravenna Crossbowmen are solid unit, but Genoese Crossbowmen are also a strong contender. However, Conquistadors are going to be more F2P friendly than other T6s because El Cid's raid is the best one to grind. Dragoons seem about equal, perhaps a bit better due to Sniper, but are not friendly for your wallet.

Ranged Cavalry is better than ranged infantry, and Mongols and Imperials are F2P choices. Mamluks are archer Templars. You get IBC with investment on Timur anyways, so IBC are more F2P friendly than Mamluks.

It depends on your war souls wealth and whether you have disposed of some fragments or not.

Melee Infantry: Royal Swordsmen, Blue Vikings/Varangians, Hengdao

Defense Infantry: Phalanx, Lombards/Swiss Halbardiers, Modao

Melee Cavalry: Camels, Siphahis (?), Teutons/Sepulchres/Black Armored (?)

Charge Cavalry: Cataphracts, Templars/Gendarmes/Jet Black

Ranged Infantry: Ravenna Elite Crossbowmen, Genoese Shielded Crossbowmen, Conquistadors/Dragoons

Ranged Cavalry: Mongols, IBC, Mamluks