Trick to winning early on is to try and avoid heavy staff salaries, resist the temptation to fill your team with young players thining you can train up players at the start, training is very tough early on, slow and costly and unlikely to reward you as you expect. Your best bet is to pick up salary efficient players (high TSP and skills and low salaries).
As you suggest you need to build your arena ready for D2. The arena trick is to build the Bleachers first, get them up to 10k but no higher until later in the game. Maximise your income by hiking your prices to the point you are about 95% full in each type of seating - this takes a bit of trial and error and the more your country and world rank goes up, the more you can charge.