This is a Forth the Three Hunters deck. I realized that the contract never stipulates that there must be three heroes, and I wanted to use Eomer in one of these decks, however his ability suggests that you want a low starting threat. Therefore, I set out on a quest to make a two character deck!
The One Ring should be played on Eomer in order to gain the full benefits of The Ring of Power. Strider will be necessary for Eomer to give him use after the quest phase. Armored Destrier can then allow him to defend. Orcrist will gain him some very helpful attack and resources and will allow him to draw an enemy to trigger his ability. Necklace of Girion can be used in much the same way. Rune Master can gain him some extra resources beyond what Orcrist offers. If Eomer gains all three of his restricted attachments, Neckmlace of Girion, and Strider, he can quest for 8.
Aragorn wants Celebrian's Stone and Armored Destrier most of all to make him capable of performing each action each round. After these, Steward of Gondor and Ancestral Armor will add some helpful resources and defense as he will be the main defender. If Aragorn gains all three of his attachments, he can quest for 7.
All the signal attachments will help to bolster stats and healing. Excess resources that may arise can also be used to transfer these cards around. Open thee Armory can be used to get to the attachments quicker. Fresh Tracks will keep enemies in the staging area so that Eomer can take them out there. Dunedain Message can be used to help get to the Side Quests quicker. Prepare for Battle will grant some very helpful card draw.