First gold general

Simeon is a good cav general (give him “immortality” and the blue horse that boosts charging rate) .
I don’t know if u have Alfred, but if I were you I’d take him asap (hero legends with great resources and a unique item that gives cav points and defence).
Then I’d move to Cnut (Halfdan if u want, just to get the naval bond which is not that bad), Hardrada of both of them.
Iustinian is pretty useful (also, but not exclusively: see in conquests) in the last hard mission campaigns to defend the cities together with Theodora (look at their economic bond; you might judge it as minuscule, but you will desperately need that little additional income to replenish garrison units).
I’ve never tried Narses, but he’s an underestimated general (I’d hire him myself in the future, just to get that tiny unit bonus provided by his bond with Belisarius).

Cnut the Great is significantly better than Hardrada. Definitely the best f2p Infantry general in the game. Moreover there is a bronze tier coin general (namely William the Iron Arm) who is almost identical to Hardrada.
Neither Basil is the best option. Unfortunately, old guides are outdated and do not reflect the current state of affairs and should be replaced sooner rather than later.

Alfred and Roland are two best f2p cavalry generals because their weapons reduce damage to these generals and this is vital for cavalry to stay alive.

Simeon is the best berserker cavalry general, who can smash enemies' lines, retreat, replenish his legion and charge again. He is the best charging general, though, as majority of cavalry generals, he is weak in defense.

Lancelot and Narses, who were labeled earlier as "sh..." by some "experts", are excellent generals when used correctly.
Probably at the moment the best compositions for them are:

For Lancelot

Ravenna crossbowmen - Woad skirmishers - Melee cavalry

Or

Ravenna crossbowmen - Woad skirmishers - Genoese Pavise crossbowmen.

Eventually it is possible to replace some parts of this legion with newly unlocked Mongolian archers etc.

For Narses

Ravenna crossbowmen - Woad skirmishers - Garrison spearmen/or any spearmen you like.

It is not a mistake to buy this or that general, but we have to analyze carefully the strength and the weakness of each general and to use them accordingly.

To some extent, yes. But usually we have more than one cavalry legions at the start of each campaign. I had a headache what to do with countless Melee cavalry units until I bought Roland. Nowadays I deploy Alfred and Roland at the start, and hire charge cavalry for Simeon (who has discounts for hiring) whenever I have an opportunity.

I guess, no-one is really "necessary". It heavily depends on the problems you solve at the moment. In campaigns generals with personal weapons are best options, because bonuses of weapons somewhat nullify the poor quality of the troops we have at our disposal. In other modes of the game it heavily depends on the level of your troops. If, for example, your Ravenna crossbowmen are lvl 12 and your Noble cavalry is only lvl 7, there is a point in deploying Lancelot, Narses and Aetius rather than Alfred and Roland.