All your assumptions thus far are pretty much correct. Bravo.
Blood of the Fallen is probably the best favor item for general usage. It just plain helps every build, i would stick with that until you are comfortable venturing into more complicated strategies. Blade of the Serpent with Torch Bearer for instance. Staff of Renewal with Regulus. BoF is really the only favor item that doesn't require more complex understanding of the game's mechanics to be useful.
Regulus is the most difficult demigod to master, and until you've MASTERED him do not play him online. You will die a lot. I realize this doesn't make any sense. If you really want to play as reg then do your research on the forums, play in a lot of noob games and be totally familiar with his skill tree and the different builds to counter different play situations.
Rook is also very difficult to play. His speed is a serious problem for new players, the best advice I can give is ALWAYS keep at least one Teleport scroll with you. Learn what the stuns and interrupts of all the demigods looks like and wait for them to be used BEFORE you attempt to teleport out. Stick with BoF until you feel comfortable moving to swift anklet or staff of renewal.
Beast is best for new players. PERIOD. You almost can't skill him bad if you tried. He has high natural armor and damage and hp, is fun and simple to play, and the best demigod in early, middle, and late game. I might get flamed for saying that last bit. But those claims are easy to support in a noob setting. The forums are chock full of great builds for this guy. In the beginning just stick with something like this:
Favor: Blood of the Fallen.
Level 1-4: Get Spit, Ooze and Inner Beast and then Ooze 2
level 5: GET FOUL GRASP!
level 6-20: Just continue getting Ooze, Inner Beast, and Diseased Claws in whatever order you want. Get ACCLIMATION, this is the most ridiculous skill in the whole game.
You may want to get more Spit. DON'T. Spit is great early game, but starts to get useless against good players late game, AND it costs a boatload of mana. Ooze, Inner beast, and diseased claws cost nothing, and are great ALL game. Foul grasp is really where most of your mana will go.
Items: Banded Armor, then Scale Mail, then Nimoth chestplate, then Unbreakable boots, then Hauberk of Life. Sell scale mail and buy slayer's wraps.
citadel: buy tower health 1 ASAP, then buy Currency 1 the SECOND war score 3 hits. After this buy priests.
I'm not trying to prescribe your behavior or strategies here, feel free to try experimenting with this build until you are comfortable moving on. But this is a great simple build that works wonders for your confidence.
Remember, play CONSERVATIVELY. Never 2v1, Do not follow demis into their base or past their towers UNLESS you have enough health to return. Dying to get a kill is almost always a bad choice. Buy the important Citadel upgrades if you can afford them. Don't count on your teammates to do it. COMMUNICATE with your teammates. PLAY CONSERVATIVELY. Dying is the worst thing you can do in a team game. DON'T DO IT. But mostly have fun.