I too started a new one last night as Charlton in League One. I hope to earn a couple of trophies in doing so.
There's one where you have to gain two consecutive promotions with a team, so going from League One to the Premier League in two seasons will unlock that.
Another is to take a 2 star or less (Charlton are 2 star) rated team and make them into a 5 star team within 5 seasons. Shouldn't be too hard as long as I get the above trophy.
My Virtual Pro is rated around 69/70, so I've put him in the side as well in an attempt to get nearer the 100 accomplishments needed.
The last one I'm looking to earn is the "no simming" trophy. To be honest, I can't be arsed playing through the cup games in the first couple of seasons. The no simming trophy is something I may look at getting if I get as far as the Premier League. I've heard there's a bug with this trophy, with some people getting it and others not. I finished a full season in FIFA 09 and didn't get awarded the trophy, so the problem still exists at times it seems. One guy on the FIFA forums said he got the trophy after just 12 games in a season...so yeah, it's pretty random.