At the start finances will probably be easier than you expect:
* You get regular cash bonuses for the first few weeks as a new manager.
* You have no salary floor for 24 weeks, meaning you can keep wage costs below normal levels.
* Winning BBM and cup matches will give you extra income for the first half of the season.
* III is filled with bots and inactive managers, leading to easier wins and bigger crowds in the future. You're a bit unlucky in this respect as III.1 has way more human managers, but on the plus side your games will be more interesting.
Gate receipts are a bit low at the start but they should soon pick up. If I remember I started with $60-70k revenue per home game, now it's $140-180k without changing division. I wouldn't advise trying to daytrade on the transfer list, it can be done but I found evaluating players difficult at the start (and still have a lot to learn).
You are right it will take a long time to max out the arena + infrastructure, but in the medium-term if you build some extra arena capacity that's all you need. Then you can slowly build the remainder over time. After a season I think you'll feel comfortable with how you are progressing