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There is plenty of room to seperate the paladin and the cleric.
Yes, 3.0e the paladin was underpowered, probably the most comparing the classes, right next to the ranger.
If you look to the next closest iteration, (3.75) Pathfinder, you find that the Paladin was actually balanced with the other classes.

I would like the return of the paladin to chivalry. By following the base chivalrous virtues, the paladin could gain the below..spread out over level progerssions 

Courage - Defending your allies and those who need defending
Justice - Hunting down your "sworn enemies"
Mercy -  sparing an enemy from death,  higher chance of gaining infomation after combat??
Generousity - Essentially Vow of poverty, or giving to those in need, would like variants, if a paladin grants half his gold to his church or charity he gains different benefits. A paladin would like to keep his sword and armor for fighting his benefactors enemies
Faith - Perhaps a miracle, a heal or disease removal, but very limited uses, 1/week??
Nobility -conveys the importance of upholding one’s convictions at all times, especially when no one else is watching.
Hope-perhaps a prayer(1/day or week) that grants a good temporary boost, to perhaps combat and non-combat uses, or perhaps before a party wipe a last resurgence of health, either to the paladin or another character.

Also
-> I don't mind spellcasting to be removed from the paladin, however I would like to see a "performance of faith" be displayed in the paladin

-> I would also like the ability to play the unarmored paladin weilding a quarterstaff. (currently 3.5e and 4.0e does not support this variant)

To note
The monk needs to be revisited. He is technically an arm of faith, not a martial-base character.