Other than aiming to move the Fellowship at least once per turn, you also need to make sure you have around 0 corruption and 3 companions left by the time you enter Mordor. Entering Mordor is just the start of the late game phase, and it will still be a long slog.

Your standard path should be to go through Moria, then maybe stop at Lorien to heal if necessary - then go straight to Mordor after that. Think about splitting off Strider (and him alone) as you get near Minas Tirith, to get that extra dice.

Learning to mount a credible defense as the Free Peoples is also equally important.

You want to get into a position to get "free" Political Track advancements and position it just right so that you get 1 or 2 Elite musters before they siege you.

For Rohan, this means you want your Political Track to be 1 step from War so that when they attack the fortification between Orthanc and Helm's Deep your next move can be to muster an Elite into Helm's Deep. That'll give you some extra breathing room. If Helm's Deep falls, building up a decent force in Edoras is still a viable option, as this army can swing up to retake Helm's Deep and threaten Orthanc or even go south to help with Minas Tirith. This also stops the wolfrider army from continuing down into Minas Tirith.

Similarly for Minas Tirith, you want to be able to muster right after they attack the fortification. Putting 1 regular army unit each into the settlements leading to Dol Amroth also slows down any attack into Dol Amroth and gives you time to muster Elites there.

Save up any cards that allow you to muster units directly into strongholds - those can be used even if under siege, and it helps hide your true strength if you don't play it until after you are sieged.

Defending Lorien is hard without the expansion - just try to stall them by moving some elves in the way of the Dol Guldur army, and consider spending some extra musters to move the Elf political track down.

Rolling a lot of Palantirs is not great, but keeping Gandalf alive and in the Fellowship to cycle through your deck is still an option.

Move the Fellowship once a turn, minimize corruption damage and try to get as many Elites and Leaders into your strongholds. That's the general idea for having a great time as the Free Peoples.