Adventuring in 4A ME:
I wouldn't remove Paladins (I always thought Dol Amroth would be crawling with them), nor take away spells from the Semi-spellcasting classes. YMMV. The entire spell list of 3.xe will have to be reworked, however. ME magic is more subtle, and 3.x's is more Flash-BOOM!
As for adventures;
Immediately after the War of the Ring, there will be plenty of cleaning up to do. Fighters, Paladins, and Rangers will be needed everywhere, and "Scouts" (Rogues) will lead the way. An expedition to free the slaves of the farms of southern Mordor might be sent out, and scouting and patrolling of Near Harad will be needed.
Dol Guldur was thrown down (by the Elves) during the WotR, and the Barad-Dur fell when Sauron did. The tower of Isengard still stands, and Tolkien tells us that Aragorn and the Fellowship later explored it, and found some goodies there...
We also know that Saruman and Grima somehow escaped, and that there are unplumbed depths, there. Rochan is weakened, and someone will need to take over this place!
A general "breeding program" will begin, immediately following the WotR, and in about 16 years, a whole new generation of heroes and heroines will emerge. The sons (and daughters!) of Rohan, especially, will be weaned to the war-songs of Kings Theoden (last of the second line), Eomer (first of the third), and the White Lady, Queen Eowyn of Osgiliath.
In the last riding of the keepers, we see that, even then, the wise did not ride through the wilderness except in great companies... Jobs for caravan guards will be aplenty... And there will be great need for those caravans! Roads, cities, fortresses, and entire lands need rebuilding! Dwarven miners and craftsmen will be flocking hither and yon!
In Gondor, King Elessar will be repairing the damage caused by the war, and Gimli and Gloin's folk will be making sure the new gates are even better than the old, and making sure the stonework, there, is as strong as Helm's Deep's. Likewise, the Elves will be planting and beautifying the place until it is fit for the Evenstar of their people.
There were many empty houses, in Minas Tirith, and as people flock to the King, these will be filled. The greatly-depleted guard will need refilling, and the nearly-decimated Rangers of Ithilien will be commanded by Lord Faramir, who will be looking for new recruits.
With Aragorn's taking of the haven's, Gondor's navy has now been more than doubled. While the rebuilding is going on, new outworks will be made, and more docks added. The Captains of War will be counselled with, and where weaknesses in Gondor's defenses were observed during the war, new works will be made, with the best minds of Elves, Dwarves, and Men working together (no doubt overseen by Gandalf, himself). The walls between Gondor and Rohan still need repairing, and men will be needed to man them.
Many families were sent away, and now must return. Many messages and embassies must be carried. Innumerable details must be attended to. While the Lords and Ladies are involved with grand, broad, over-arching plans, someone else must carry out the minute details...
And there are all of those things lost and forgotten... Gandalf and Faramir spent long in the libraries of Gondor, and Gandalf tells us that there are things there which few men can now read... Besides the method for determining The One Ring, what other secrets lie, long forgotten, hidden in some ancient script?
And the hordes of Mordor? While things made by the Ring are undone (and things upheld by the lesser rings also fading - hence no more Nazgul!), not everything which was made was made by the Ring! When the Barad-Dur fell, and Mount Doom erupted, the Black Gates suffered no harm, nor did the slave-labor camps of the south, nor Minas Morgul (which we're told would be vacant for many lives of men). Shelob's fate is unclear, but her fear remains. Mordor is uncleansed...
And Aragorn, the foresighted, tells Eomer that their swords will meet on the field of battle, again. Indeed, the appedices tell us that wars with Harad and Khand will continue... How many more harrowing trails will King Elessar lead his troops on, like the climb up Mount Carathras, the trek through Khazad-Dum, and the Ride along the Paths of the Dead?
And then, the embassies to peoples... What will becomes of the Ents? Will any Hobbit ever remember that, even before they hit Bree, that "a walking tree" was seen near the Shire? Is it an Entwife, and if so, can she be found?
Two decades after the WotR, most of the kingdom will not be in disrepair, but will still be rebuilding. While most of the Noldor Elves will be gone, we know that there are still a few left at the Grey Havens. Even after they leave, Elrohir and Elladan (and probably a few of their people) will keep Rivendell alive while they continue their war with the Orcs... And we know that the Misty Mountains are FULL of caves of them!
And then there are all those barrows full of undead things which might still need cleaning out. And those blades of Westernesse to be collected. And those swords from ancient, long-sunken Gondolin to be investigated! (Hmmm! I'm pretty sure Gandalf wouldn't have needed that in Valinor... So who do you think he left it with?)
Mirkwood is also in need of a great cleansing... Greenwood the Great it will be, again, someday, and Sylvan Elves and woodsmen will hunt the giant, intelligent spider folk through the trees until they are no more.
And with the depletion of Rohan, perhaps some of their former people, from far to the north, will be sent for, to strengthen the land. Here's a good intro for Barbarians.
And Rhun? And the Woses? And the Balchoth? And the Wainriders? And the Istarii? (What ever happened to Radagast, anyway?)
Looking even further along, what to do with Mordor? Some parts of it are good (down near the Sea of Nurn), and Aragorn eventually cedes it to those who were forced to labor, there... What of the rest of it? Are the towers cleansed? Are the tunnels of Cirith Ungol ever cleansed? How long does Minas Morgul remain uninhabited? How long before it is investigated, like Minas Ithil was?
And what is done with Harad and Khand, once there are pacified? Are they ruled by Gonorians? Do men of Nurn hunt the Kine of Araw in Rhune? Is Fangorn inhabited by Entings? Does Annuminas explore the ruins of Angmar? And what is to be done with it?
Eventually, Gandalf, Frodo, Legolas, Gimli, and perhaps Samwise will pass over the seas... Boromir is already dead, and Merry, Pippin, Aragorn, and Arwen will be, in time... Before then, will they reach out to other people, like the Lossoth who once harbored some of Aragorn's distant kin? How close will any ties be? Will Khand and Harad be a problem, then? Will the Wilderlands be safe, by then? If so, will they remain that way?
By this time, relations between Dwarves, Elves, and Men will be better. During the reign of Elessar's son, they will probably remain so. But after that? After the passing(s) of the keepers?
Elladan and Elrohir will continue their fight for as long as Orcs are a problem... Will they all be cleared out, by then? And if so, then what? Can they pass over the seas? How many of them remain after Elrond leaves, anyway?
And Greenwood? Is it cleansed, or still murky? And does it get better, or worse, after that? And the folk of Thranduil? They were none too friendly, in The Hobbit. Will that be much changed?
And Khazad-Dum? Will Durin's Door reopen? Will Mithril flow, once again? Is the power of the Orcs broken without the Balrog? And what will the Wizard-less world do, if another is awakened, there?
And how many strange remnants of past ages will be encountered in unexpected places? Like Arwain-Ben-Adar and Goldberry in a little patch of forest, or swords of ancient Gondolin in a troll's cave? Are there still dragons in the Withered Heath? Other Moriquendi in the south and east?
As Middle Earth ages, we know that the Ents will eventually become more or less dormant, and Hobbits eventually fade away... Elves and Dwarves will also either cease to be, or be so hidden as to become legend... How, why, and when is unknown.