I don't really follow the games enough to have a favourite team, so does anyone have any suggestions or stuff like that? I remember Brad interviewed team liquid and stuff for starcraft.

Or should I just choose the favourite team most likely to win the competition and get the bonuses that come with that, and what is the favourite team?

If i'm not mistaken, the Team Cup does not give you anything. Every compendium match (The matchmaking with prepicked heroes) you win gives points to your favorite team and player, and at the end of each week, the ones with the most points get Dota2 items with a special rarity (displayed on the right page).
The tournament prediction segment of the compendium has a 'winner' prediction that you can fill out, although I am unaware of what the rewards will be.

As for the choice of a team, you can find the results of recent matches on dota2lounge, and check the prior performances of the teams in tournaments via the Dota 2 wiki.

Well, Alliance have been dominating everybody over the past few months, so they're probably your safest bet as far as Winner prediction.

Obviously things can change though, and everyone has bad games/bad days, so who can really say who'll end up winning. I think Alliance are the hands-down favorite, though.

I really like Quantic and Alliance, they feel slightly more unorthodox than most other teams while still staying effective. "Incredibly effective in Alliance case".

Fan favorite Na'vi is of course always a hoot, if anything because the commentators and live chat go wild for that shit.