Not trying to be mean but why are you asking random people on the internet how you should start your career mode? Whatever team or club you like then choose them. Pick a lesser team and work your way up. There is no wrong choice and if you dont like the option you picked you can always start over :)
I always start with a team in a second division and try to promote them and then win the title in the top division. You will have a very small budget of course, you will need to rely on good scouted players and make good use of the little money you get .
This year I am starting with Villarreal, they were my favorite La Liga team, should be fun taking back to the top.
Goal this year is to take Rochdale AFC from league 2 all the way to the Premier League. I will be attempting this without using the financial takeover at first but I can't say I won't cheat a bit and bring in a billionaire owner when I reach the championship.
I believe it is more fun this way. But that's just me. I am a huge Arsenal fan but I never use them in FIFA because it's fun to try and achieve promotion 3 times instead of starting at the top already.