I know next-to-nothing about this brand of football, but here's my picks based on sheer guesswork:
GK--Watcher in the Water (Moria)
DF--Beren (Doriath)
DF--Glorfindel (Rivendell)
DF--Luthien(Doriath)
MF--Gwaihir (Misty Mountains)
Maedhros (Tuna)
The Phantom (Barrow-Downs)
MF--Dwalin (Misty Mountains)
FW--Mormegil (Nargothrond)
FW--Saucepan Man (Barrow-Downs)
EDIT: This team reflects changes made before the matches played on July 18th
The Watcher in the Water is a natural goalkeeper -- between size, strength, and all those arms, he should prove a worthy adversary.
For defenders I chose the husband-wife team of Beren and Luthien for their skill in stealing the prize from even the strongest of adversaries, and Glorfindel of Rivendell for his ability to get through tough situations against multiple opponents.
At midfield, the Gandalf-Gwaihir pairing seemed like a good combination of speed and experience. Balance that out with Quickbeam as the steady power-player, Legolas for dexterity, and Sam for gritty stick-to-it-iveness, I believe I have a formidable center.
Finally, a pair of unusual picks at forward. Tulkas seems more like a defender-type, but I am casting against type here because I believe that Tulkas will be able to dominate his way around (and through!) most defenders. Frodo is the exact opposite of Tulkas -- small, relatively weak, and with a demonstrated tendency to slip and make mistakes right at the scoring opportunity. However, with faithful Sam at midfield, he should be able to obtain the goal.
Let the games begin!